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Well-behaved sequence in a commutative ring
In commutative algebra, a regular sequence is a sequence of elements of a commutative ring which are as independent as possible, in a precise sense. This
Regular_sequence
Infinite sequence in mathematics
In mathematics the regular paperfolding sequence, also known as the dragon curve sequence, is an infinite sequence of 0s and 1s. It is obtained from the
Regular_paperfolding_sequence
Sequence of points that get progressively closer to each other
In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given
Cauchy_sequence
Finite or infinite ordered list of elements
Constant-recursive sequence Geometric progression Harmonic progression Holonomic sequence Regular sequence Pseudorandom binary sequence Random sequence Related concepts
Sequence
Mathematical sequence
k-regular sequence is a sequence satisfying linear recurrence equations that reflect the base-k representations of the integers. The class of k-regular
K-regular_sequence
Topics referred to by the same term
which can be represented over any field Regular paperfolding sequence, also known as the dragon curve sequence Regular tree grammar Castelnuovo–Mumford regularity
Regular
Construction in homological algebra
can be used to tell when a set of elements of a (local) ring is an M-regular sequence, and hence it can be used to prove basic facts about the depth of a
Koszul_complex
Sequence of characters that forms a search pattern
A regular expression (shortened as regex or regexp), sometimes referred to as a rational expression, is a sequence of characters that specifies a match
Regular_expression
Infinite sequence of terms characterized by a finite automaton
theoretical computer science, an automatic sequence (also called a k-automatic sequence or a k-recognizable sequence when one wants to indicate that the base
Automatic_sequence
Topics referred to by the same term
An M-sequence may refer to: Regular sequence, which is an important topic in commutative algebra. A maximum length sequence, which is a type of pseudorandom
M-sequence
when two ⟨cs⟩ are brought together in a compound word, they form the regular sequence ⟨cscs⟩. ⟨chd⟩ is used for /dʒ/ in Eskayan romanised orthography and
List of Latin-script trigraphs
List_of_Latin-script_trigraphs
These characters appear in the American animated television series Regular Show, created by J. G. Quintel for Cartoon Network. The series revolves around
List of Regular Show characters
List_of_Regular_Show_characters
Part of a spectrum
in a regular sequence that appears to be a band. It is a colored band, separated by dark spaces on the two sides and arranged in a regular sequence. In
Spectral_band
Visualisation of computer system processes
alternative scenarios. There are two kinds of sequence diagrams: Sequence Diagram (SD): A regular version of sequence diagram describes how the system operates
Sequence_diagram
Equiangular and equilateral polygon
limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon
Regular_polygon
ideal of X ∩ U {\displaystyle X\cap U} is generated by a regular sequence of length r. A regular embedding of codimension one is precisely an effective
Regular_embedding
Numbers that evenly divide powers of 60
Several other sequences at the On-Line Encyclopedia of Integer Sequences have definitions involving 5-smooth numbers. Although the regular numbers appear
Regular_number
Tool in mathematical dimension theory
by a regular sequence of k polynomials has a codimension of k, and that its degree is the product of the degrees of the polynomials in the sequence. Every
Hilbert series and Hilbert polynomial
Hilbert_series_and_Hilbert_polynomial
Numbers obtained by adding the two previous ones
Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known
Fibonacci_sequence
Infinite sequence of numbers satisfying a linear equation
linear recurrence sequence, linear-recursive sequence, linear-recurrent sequence, or a C-finite sequence. For example, the Fibonacci sequence 0 , 1 , 1 , 2
Constant-recursive_sequence
Mathematical sequence involving arithmetic progressions
In mathematics, a Stanley sequence is an integer sequence generated by a greedy algorithm that chooses the sequence members to avoid arithmetic progressions
Stanley_sequence
Place of public bathing common in Muslim societies
evolved from the layout of Roman and Greek bathhouses and featured a regular sequence of rooms: an undressing room, a cold room, a warm room, and a hot room
Hammam
Poem by John Donne
three stanzas rhyming ABABCCDDD, with lines that vary in length in a regular sequence. The first stanza demands a variety of impossible feats and the second
Go_and_Catch_a_Falling_Star
Room with a hot plunge bath, used in a Roman bath complex
by a furnace tended by slaves. It was also the hottest room in the regular sequence of bathing rooms; after the caldarium, bathers would progress back
Caldarium
On polynomial rings over fields
generated by a regular sequence of homogeneous polynomials. In particular, the sequence x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} is regular, and the
Hilbert's_syzygy_theorem
Study of dimension in algebraic geometry
{\displaystyle M} -regular sequence, then x 1 j , … , x n j {\displaystyle x_{1}^{j},\dots ,x_{n}^{j}} is also an M {\displaystyle M} -regular sequence for each
Dimension_theory_(algebra)
Lists of values of mathematical functions
significant memory to store the table. The other possibility, since a regular sequence of values is required, is to use a recurrence formula to compute the
Trigonometric_table
Number, sum of distinct powers of 4
Moser–de Bruijn sequence to be calculated from earlier values, and can be used to prove that the Moser–de Bruijn sequence is a 2-regular sequence. The numbers
Moser–de_Bruijn_sequence
m = s(n). The class of k-synchronized sequences lies between the classes of k-automatic sequences and k-regular sequences. Let Σ be an alphabet of k symbols
K-synchronized_sequence
Type of prime number
Unsolved problem in mathematics Are there infinitely many regular primes, and if so, is their relative density e − 1 / 2 {\displaystyle e^{-1/2}} ? More
Regular_prime
Natural number
"Sequence A000043 (mersenne prime exponents)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A003273
5
Exact sequence used to describe the structure of an object
resolution is given by the Koszul complex of a regular sequence in a local ring or of a homogeneous regular sequence in a graded algebra finitely generated over
Resolution_(algebra)
Structured system of communication
to acquire an art". First language acquisition proceeds in a fairly regular sequence, though there is a wide degree of variation in the timing of particular
Language
Class of languages studied in formal language theory in computer science
between a and b), ω-regular languages accept infinite words (such as, infinite sequences beginning in an a, or infinite sequences alternating between
Omega-regular_language
Type of cardinal number in mathematics
countable cardinal numbers, and is regular. ℵ ω {\displaystyle \aleph _{\omega }} is the next cardinal number after the sequence ℵ 0 {\displaystyle \aleph _{0}}
Regular_cardinal
Natural number
(ed.). "Sequence A001748 (a(n) = 3 * prime(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A005100
15_(number)
is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. OEIS core sequences Index to OEIS
List_of_integer_sequences
Ordered list of whole numbers
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula
Integer_sequence
Mathematical analysis
regular sequence are more than 3 2 {\displaystyle {\tfrac {3}{2}}} apart and so one may compute natural numbers exceeding any real. For the regular sequences
Constructive_analysis
parameters for R is a regular sequence on W. Cohen-Macaulayness of Direct Summands Conjecture. If R is a direct summand of a regular ring S as an R-module
Homological conjectures in commutative algebra
Homological_conjectures_in_commutative_algebra
Measure of a mathematical object studied in the field of algebraic geometry
embedded in an affine or projective space. The maximal length of a regular sequence in the coordinate ring A. This the algebraic translation of the preceding
Dimension of an algebraic variety
Dimension_of_an_algebraic_variety
Value to which tends an infinite sequence
In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the lim {\displaystyle \lim } symbol
Limit_of_a_sequence
Substance composed of macromolecules with repeating structural units
Periodic copolymers have more than two species of monomer units in a regular sequence. Statistical copolymers have monomer residues arranged according to
Polymer
Continuous band of stars that appears on plots of stellar color versus brightness
In astronomy, the main sequence is a classification of stars which appear on plots of stellar color versus brightness as a continuous and distinctive band
Main_sequence
Natural number, composite number
Sloane, N. J. A. (ed.). "Sequence A238822 (Number of equilateral triangles bounded by the sides and diagonals of a regular 3n-gon.)". The On-Line Encyclopedia
14_(number)
Tool in homological algebra
spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and
Spectral_sequence
Natural number
N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)"
22_(number)
Mathematical category with finite limits and coequalizers
{(f,-f)}}Y\to 0} is a short exact sequence in the usual sense. A functor between regular categories is called regular, if it preserves finite limits and
Regular_category
Result concerning ideals of commutative rings
{depth} _{A}(I,M)} = the maximal length of M-regular sequences in I = the length of every maximal M-regular sequence in I. Then d ≤ n {\displaystyle d\leq n}
Prime_avoidance_lemma
Algorithms for computing Gröbner bases
bases for a large class of interesting polynomial systems, called regular sequences, without ever simplifying a single polynomial to zero—the most time-consuming
Faugère's F4 and F5 algorithms
Faugère's_F4_and_F5_algorithms
Galaxy morphological classification scheme advocated by Edwin Hubble
2536, NGC 2903. Galaxies that do not fit into the Hubble sequence, because they have no regular structure (either disk-like or ellipsoidal), are termed
Hubble_sequence
element of M. 5. A regular sequence with respect to some module M is a sequence of elements a1,a2,...,an of R such that each am+1 is regular for the module
Glossary of commutative algebra
Glossary_of_commutative_algebra
Degree of variation of a trading price series over time
ensemble returns instead of time series of returns. Another considers the regular sequence of directional-changes as the proxy for the instantaneous volatility
Volatility_(finance)
Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A070169 (Rounded total surface area of a regular tetrahedron with edge
1000_(number)
British novelist (1913–1998)
RAF Wunstorf during the Berlin Airlift. Innes produced books in a regular sequence, with six months of travel to settings all over the world and research
Hammond_Innes
Algebraic structure
number of elements in some (or, as can be shown, any) maximal regular sequence, i.e., a sequence a1, ..., an ∈ m such that all ai are non-zero divisors in
Commutative_ring
Natural number
Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-09. Grünbaum, Branko; Shepard, Geoffrey (November 1977). "Tilings by Regular Polygons" (PDF)
7
Embedding of the unit interval into 3-space ambient isotopy inequivalent to a line segment
generally referred to as the Fox-Artin wild arc. The crossings have the regular sequence over/over/under/over/under/under when following the curve from left
Wild_arc
Pair of integers related by their divisors
(m, n) is said to be regular (sequence A215491 in the OEIS); otherwise, it is called irregular or exotic. If (m, n) is regular and M and N have i and
Amicable_numbers
Invariant of rings and modules
David Rees, the depth can also be characterized using the notion of a regular sequence. Suppose that R {\displaystyle R} is a commutative Noetherian local
Depth_(ring_theory)
Natural number
42-sided tetracontadigon is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane. 42 is
42_(number)
Natural number
(ed.). "Sequence A094133 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A094133
17_(number)
Term in mathematics
into regular sequence terms, allowing the definition of local complete intersection, or after some localization an ideal has defining regular sequences. Since
Complete_intersection
Worst-case number of comparisons used by sorting algorithms
)}+A{\bigl (}\lceil n/2\rceil {\bigr )}+n-1} . It is an example of a 2-regular sequence. Asymptotically, the value of the n {\displaystyle n} th sorting number
Sorting_number
Device or software that records, edits or plays back musical notes
A music sequencer (or audio sequencer or simply sequencer) is a device or application software that can record, edit, or play back music, by handling
Music_sequencer
Concept in geometry
viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides. The area of a regular polygon is half its perimeter multiplied
Area_of_a_circle
mathematics, a Følner sequence for a group is a sequence of sets satisfying a particular condition. If a group has a Følner sequence with respect to its
Følner_sequence
Quality of movement of a dog
body at all times, each foot lifting from the ground one at a time in regular sequence. Amble A relaxed, easy gait in which the legs on either side move almost
Canine_gait
Construction in homological algebra
when the first module is the quotient of a commutative ring by any regular sequence, using the Koszul complex. For example, if R {\displaystyle R} is the
Ext_functor
Subdivision of the plane into polygons that are all regular
Dimensions. Dover Publications. Chapter X: The Regular Polytopes Préa, P. (1997). "Distance sequences and percolation thresholds in Archimedean Tilings"
Euclidean tilings by convex regular polygons
Euclidean_tilings_by_convex_regular_polygons
Music sequencer constructed from analog electronics
An analog sequencer is a music sequencer constructed from analog electronics, invented in the first half of the 20th century. Raymond Scott designed and
Analog_sequencer
Polygon shape with eight sides
ὀκτάγωνον (oktágōnon) 'eight angles') is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular
Octagon
Aspect of music
ritual. The establishment of a basic beat requires the perception of a regular sequence of distinct short-duration pulses and, as a subjective perception of
Rhythm
Solid with 12 equal pentagonal faces
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron (a polyhedron with 12 faces) composed of regular pentagonal faces, three meeting at
Regular_dodecahedron
Circular depression in a solid astronomical body formed by the impact of a smaller object
crater. Complex-crater morphology on rocky planets appears to follow a regular sequence with increasing size: small complex craters with a central topographic
Impact_crater
Construction in homological algebra
Tor groups that involve the quotient of a commutative ring by any regular sequence, using the Koszul complex. For example, if R {\displaystyle R} is the
Tor_functor
Number of edges touching a vertex in a graph
1, 0). The degree sequence is a graph invariant, so isomorphic graphs have the same degree sequence. However, the degree sequence does not, in general
Degree_(graph_theory)
Long exact sequence
field of mathematics known as algebraic topology, the Gysin sequence is a long exact sequence which relates the cohomology classes of the base space, the
Gysin_homomorphism
Polygon with 12 edges
In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon. A regular dodecagon is a figure with sides of the same length and internal angles of
Dodecagon
Natural number between 89 and 91
A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29. Sloane, N. J. A. (ed.). "Sequence A022008 (Initial
90_(number)
Register that stores where in a program a processor is executing
execution and prepare subsequent instructions for execution outside the regular sequence. Modern high-level programming languages still follow the sequential-execution
Program_counter
Most common variant of a genetic sequence across samples
molecular biology and bioinformatics, the consensus sequence (or canonical sequence) is the calculated sequence of most frequent residues, either nucleotide
Consensus_sequence
Formal language that can be expressed using a regular expression
language L is a rational function if L is regular. Hence for every regular language L {\displaystyle L} the sequence s L ( n ) n ≥ 0 {\displaystyle s_{L}(n)_{n\geq
Regular_language
Four-dimensional analogues of the regular polyhedra in three dimensions
mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra
Regular_4-polytope
with the old logo, CDT, was followed by CFT and then CFS. After that, regular sequence resumed: CDV through CFR, then (since CFS and CFT have already been
Vehicle registration plates of Alberta
Vehicle_registration_plates_of_Alberta
Type of dance with preset movement pattern
Doble, Bossa Nova, Salsa, Mambo. Regular competitions are held between dance teachers to decide which newly created sequence dances shall be officially adopted
Sequence_dance
Four-dimensional analogue of the cube
in a sequence of regular 4-polytopes and honeycombs, {p,3,3} with tetrahedral vertex figures, {3,3}. The tesseract is also in a sequence of regular 4-polytope
Tesseract
In-camera visual effects process
photography to view the combined sequence live, allowing for such effects to be filmed more like a regular sequence, and the performers could be specifically
Front_projection_effect
Part of an animal that coordinates actions and senses
stimulus. Neurons were found to be capable of producing regular sequences of action potentials, or sequences of bursts, even in complete isolation. When intrinsically
Nervous_system
Ethnic group of Tanzania
year to year and from place to place. Across the region, there is a regular sequence of soil and vegetation zones. The upper levels are dry woodland typified
Sukuma_people
Natural number
smallest perfect number. A six-sided polygon is a hexagon, one of the three regular polygons capable of tiling the plane. A hexagon also has 6 edges as well
6
Large impact craters with uplifted centres
crater. Complex-crater morphology on rocky planets appears to follow a regular sequence with increasing size: small complex craters with a central topographic
Complex_crater
Natural number
trihexagonal tiling. A regular dodecahedron has twelve pentagonal faces. Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have
12_(number)
Regular semantics is a computer hardware consistency model. It describes a type of guarantee provided by a processor register that is shared by several
Regular_semantics
Hypothetical former Solar System planet
have once existed between Mars and Jupiter. After learning of the regular sequence discovered by the German astronomer and mathematician Johann Daniel
Phaeton_(hypothetical_planet)
Construct in algebraic geometry
{\displaystyle B=A/I} , and I {\displaystyle I} is generated by a regular sequence, then I / I 2 {\displaystyle I/I^{2}} is a projective module and L
Cotangent_complex
Solid with twenty equal triangular faces
The regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from a pentagonal antiprism by attaching two pentagonal
Regular_icosahedron
Direct summand of a free module (mathematics)
given by the Koszul complex of a regular sequence, which is a free resolution of the ideal generated by the sequence. The length of a finite resolution
Projective_module
Narrative technique used in television and films
having to introduce the regular characters, or even the series synopsis, which would typically be outlined in the title sequence itself. British producer
Cold_open
the Koszul resolution for the quotient R/(x1, ...., xn) of R by a regular sequence of elements. Friedemann Brandt, Glenn Barnich, and Marc Henneaux (2000)
Koszul–Tate_resolution
REGULAR SEQUENCE
REGULAR SEQUENCE
Male
Italian
Italian form of German Reginar, RANIERO means "wise warrior."
Girl/Female
Muslim/Islamic
One who remembers Allah regularly
Girl/Female
Muslim
One who remembers Allah regularly
Girl/Female
Hebrew
Precious.
Girl/Female
Indian
One who remembers Allah regularly
Male
German
A derivative of German Reginar, RAINER means "wise warrior."
Surname or Lastname
English, of Welsh origin
English, of Welsh origin : variant of Bevan, with the addition of the regular English patronymic suffix -s.
Girl/Female
Arabic, Muslim
Pilgrimage to Makkah Other than Regular Hajj Days
Surname or Lastname
North German
North German : variant of Asch.English : variant spelling of Ash (asche was the regular Middle English spelling of this word).
Surname or Lastname
English
English : nickname probably for a tenant whose feudal obligations included a regular payment in cash or kind (for example bread or salt) of a halfpenny.
Boy/Male
Hindu, Indian, Tamil
Regular Winner
Surname or Lastname
English (Devon)
English (Devon) : unexplained. Possibly an irregular variant of Birchall.
Male
Spanish
Spanish form of Roman Latin Regulus, RÉGULO means "ruler."
Surname or Lastname
English, of Welsh origin
English, of Welsh origin : variant of Bowen, with the addition of the regular English patronymic suffix -s.Altered spelling of Dutch Bouwens, a variant of Bauwens.
Boy/Male
Indian, Sanskrit
Connector; Regulator
Male
Scandinavian
Scandinavian form of German Reginar, RAGNAR means "wise warrior."
Boy/Male
Gujarati, Haryanvi, Hindu, Indian, Kannada, Marathi, Telugu
Regular; Ethical; Good in Nature
Boy/Male
Shakespearean
King Henry IV, Part 1 and 2' An irregular humorist.
Boy/Male
Hindu, Indian, Traditional
Conduct; Regular Performance of Worship
Boy/Male
Shakespearean
King Henry IV, Part 1 and 2' Edward Poins, an irregular humorist.
REGULAR SEQUENCE
REGULAR SEQUENCE
Female
Italian
Feminine form of Italian Savino, SAVINA means "Sabine; a follower of another religion."
Girl/Female
Hindu, Indian, Marathi
A Small Diamond
Boy/Male
Biblical
Sheaf of corn.
Female
Finnish
Finnish name TUIJA means "cedar."
Female
Basque
, faith.
Girl/Female
Latin
Dawn.
Boy/Male
Indian
Merciful; Patient
Boy/Male
Hindu, Indian, Punjabi, Sikh, Tamil
Shiva's Wife
Girl/Female
Tamil
Loka Priya | லோக  பà¯à®°à®¿à®¯Â
Lustrous
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Collection
REGULAR SEQUENCE
REGULAR SEQUENCE
REGULAR SEQUENCE
REGULAR SEQUENCE
REGULAR SEQUENCE
pl.
of Tegula
a.
Thorough; complete; unmitigated; as, a regular humbug.
a.
Measured by an angle; as, angular distance.
a.
Constituted, selected, or conducted in conformity with established usages, rules, or discipline; duly authorized; permanently organized; as, a regular meeting; a regular physican; a regular nomination; regular troops.
n. pl.
A division of Echini which includes the circular, or regular, sea urchins.
a.
Of or pertaining to a tile; resembling a tile, or arranged like tiles; consisting of tiles; as, a tegular pavement.
a.
Fig.: Lean; lank; raw-boned; ungraceful; sharp and stiff in character; as, remarkably angular in his habits and appearance; an angular female.
n.
One who is not regular; especially, a soldier not in regular service.
a.
Governed by rule or rules; steady or uniform in course, practice, or occurence; not subject to unexplained or irrational variation; returning at stated intervals; steadily pursued; orderlly; methodical; as, the regular succession of day and night; regular habits.
n.
A secular ecclesiastic, or one not bound by monastic rules.
a.
Of or pertaining to the jugular vein; as, the jugular foramen.
a.
Conformed to a rule; agreeable to an established rule, law, principle, or type, or to established customary forms; normal; symmetrical; as, a regular verse in poetry; a regular piece of music; a regular verb; regular practice of law or medicine; a regular building.
a.
Belonging to a monastic order or community; as, regular clergy, in distinction dfrom the secular clergy.
pl.
of Regulus
a.
Not regular; not conforming to a law, method, or usage recognized as the general rule; not according to common form; not conformable to nature, to the rules of moral rectitude, or to established principles; not normal; unnatural; immethodical; unsymmetrical; erratic; no straight; not uniform; as, an irregular line; an irregular figure; an irregular verse; an irregular physician; an irregular proceeding; irregular motion; irregular conduct, etc. Cf. Regular.
a.
Irregular in position; having no regular order; as, scattered leaves.
a.
Not regular; not bound by monastic vows or rules; not confined to a monastery, or subject to the rules of a religious community; as, a secular priest.
a.
Having all the parts of the same kind alike in size and shape; as, a regular flower; a regular sea urchin.
adv.
In a regular manner; in uniform order; methodically; in due order or time.
v. t.
To cause to become regular; to regulate.