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mathematical logic, the De Bruijn notation is a syntax for terms in the λ calculus invented by the Dutch mathematician Nicolaas Govert de Bruijn. It can be seen
De_Bruijn_notation
Mathematical notation in lambda calculus
In mathematical logic, the de Bruijn index is a tool invented by the Dutch mathematician Nicolaas Govert de Bruijn for representing terms of lambda calculus
De_Bruijn_index
Dutch mathematician (1918–2012)
Nicolaas Govert "Dick" de Bruijn (Dutch: [ˈnikoːlaːs ˈxoːvər də ˈbrœyn]; 9 July 1918 – 17 February 2012) was a Dutch mathematician, noted for his many
Nicolaas_Govert_de_Bruijn
Surname list
constant related to the Riemann zeta-function De Bruijn notation, a syntax for terms in the λ calculus De Bruijn's theorem, a theorem regarding the packing
De_Bruijn
Cycle through all length-k sequences
In combinatorial mathematics, a de Bruijn sequence of order n on a size-k alphabet A is a cyclic sequence in which every possible length-n string on A
De_Bruijn_sequence
Mathematical-logic system based on functions
correspondence between programs and proofs De Bruijn index – notation disambiguating alpha conversions De Bruijn notation – notation using postfix modification functions
Lambda_calculus
Describes approximate behavior of a function
abuse of notation, since the use of the equals sign could be misleading as it suggests a symmetry that this statement does not have. As de Bruijn says, O
Big_O_notation
Mathematical function
In analytic number theory, the Dickman function or Dickman–de Bruijn function ρ is a special function used to estimate the proportion of smooth numbers
Dickman_function
syntactic, semantic, and computational constituents. Syntax is based on de Bruijn’s notation, which overcomes the difficulties of using bound variables. The evaluations
Categorical_abstract_machine
Relationship between programs and proofs
year before Howard's manuscript started circulating. N. G. de Bruijn used the lambda notation for representing proofs of the theorem checker Automath, and
Curry–Howard_correspondence
n ) {\displaystyle O(n/\log n)} , as expressed using big O notation. For binary de Bruijn sequences, no better length is possible. The (decision version
Smallest_grammar_problem
Description of limiting behavior of a function
{\displaystyle f(x)\sim g(x)\quad ({\text{as }}x\to \infty )} if and only if (de Bruijn 1981, §1.4) lim x → ∞ f ( x ) g ( x ) = 1. {\displaystyle \lim _{x\to
Asymptotic_analysis
avoid variable names altogether by using a so-called "name-free" De Bruijn index notation. Explicit substitutions were sketched in the preface of Curry's
Explicit_substitution
Eleventh letter in the Greek alphabet
von Mangoldt function in mathematical number theory. Lambda denotes the de Bruijn–Newman constant which is closely connected with Riemann's hypothesis.
Lambda
Topics referred to by the same term
station, a railway station in Tangerang, Indonesia (station code PI) Pi de Bruijn (born 1942), Dutch architect Pi O or П. O. (born 1951), Greek-Australian
Pi_(disambiguation)
Field of mathematics which studies incidence structures
the Hesse configuration. A related result is the de Bruijn–Erdős theorem. Nicolaas Govert de Bruijn and Paul Erdős proved the result in the more general
Incidence_geometry
Symbols for constants, special functions
mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Mathematical set with repetitions allowed
and therefore the cardinality of this multiset is 6. Nicolaas Govert de Bruijn coined the word multiset in the 1970s, according to Donald Knuth. However
Multiset
Numbers whose differences are not squares
Another square-difference-free set is obtained by doubling the Moser–de Bruijn sequence. The best known upper bound on the size of a square-difference-free
Square-difference-free_set
Austrian-Canadian mathematician
1970) was an Austrian-Canadian mathematician, best known for his polygon notation. A native of Vienna, Leo Moser immigrated with his parents to Canada at
Leo_Moser
Board game for one player
Article 08.4.8, arXiv:math.CO/0703865, Bibcode:2007math......3865B. Bruijn, N.G. de (1972), "A solitaire game and its relation to a finite field" (PDF)
Peg_solitaire
Reference sequence of human mitochondrial DNA
Information. Retrieved on 30 January 2016. Anderson S, Bankier AT, Barrell BG, de Bruijn MH, Coulson AR, Drouin J, Eperon IC, Nierlich DP, Roe BA, Sanger F, Schreier
Cambridge_Reference_Sequence
Field of combinatorics using complex analysis
followed. Wikibooks has a book on the topic of: Analytic Combinatorics De Bruijn, N.G. (1981). Asymptotic Methods in Analysis. Dover Publications. Flajolet
Analytic_combinatorics
Count of the possible partitions of a set
n)^{2}}}\right)\\&{}\qquad {\text{as }}n\to \infty \end{aligned}}} was established by de Bruijn 1981. Gardner 1978 raised the question of whether infinitely many Bell
Bell_number
objectives." A number of other constructions have been given, by: de Bruijn (1976), de Bruijn (1977) Rieger (1982) Knopfmacher & Knopfmacher (1987), Knopfmacher
Construction of the real numbers
Construction_of_the_real_numbers
Non-periodic tiling of the plane
Scientific American. In 1981, N. G. de Bruijn provided two different methods to construct Penrose tilings. De Bruijn's "multigrid method" obtains the Penrose
Penrose_tiling
also a Friedman number. 1025 = Proth number 210 + 1; member of Moser–de Bruijn sequence, because its base-4 representation (1000014) contains only digits
1000_(number)
precision. The constant in the Berry–Esseen Theorem: 0.4097 < C < 0.4748 De Bruijn–Newman constant: 0 ≤ Λ ≤ 0.2 Chaitin's constants Ω, which are transcendental
List_of_numbers
Theoretical model of computation
presentation of the Krivine machine given here is based on notations of lambda terms that use de Bruijn indices and assumes that the terms of which it computes
Krivine_machine
Type of number sequence
the sequence is countable, so f is zero almost everywhere. In fact, the de Bruijn–Post Theorem states the converse of the above criterion: If f is a function
Equidistributed_sequence
Theoretical computer model
machine in OCaml, representing lambda terms with de Bruijn indices: type term = IND of int (* de Bruijn index *) | ABS of term | APP of term * term Values
CEK_Machine
Mathematical formalism
\lambda y.\lambda y.y} , which is not at all the same. In the De Bruijn index notation, any two α-equivalent terms are syntactically identical, and confusion
Lambda_calculus_definition
Method of DNA sequence reconstruction
typical of the Sanger-data assemblers and relies on an overlap graph; de Bruijn Graph (DBG) approach, which is most widely applied to the short reads
Sequence_assembly
Set of points on a line segment with certain topological properties
Knaster–Kuratowski fan List of fractals by Hausdorff dimension Moser–de Bruijn sequence Smith, Henry J.S. (1874). "On the integration of discontinuous
Cantor_set
Base-4 numeral system
DFS V high-resolution site survey systems. Conversion between bases Moser–de Bruijn sequence, the numbers that have only 0 or 1 as their base-4 digits Beeler
Quaternary_numeral_system
Computer science and recursion theory
recursive functions (cf Boolos-Burgess-Jeffrey 2002:74-77). Association list De Bruijn index McCarthy 1959. McCarthy 1960. Minsky (1967) does not include the
McCarthy_Formalism
Elementary cellular automaton
332–336, doi:10.1090/S0002-9939-1975-0386350-1 Sutner, Klaus (1991), "De Bruijn Graphs and Linear Cellular Automata" (PDF), Complex Systems, 5: 19–30
Rule_90
Ordering of binary values, used for positioning and error correction
The Gray code nature is useful (compared to chain codes, also called De Bruijn sequences), as only one sensor will change at any one time, so the uncertainty
Gray_code
Type whose definition depends on a value
is an extension of propositional logic, adding quantifiers. Howard and de Bruijn extended lambda calculus to match this more powerful logic by creating
Dependent_type
On chains and antichains in partial orders
subset S of P has a w-colorable incomparability graph. Therefore, by the De Bruijn–Erdős theorem, P itself also has a w-colorable incomparability graph,
Dilworth's_theorem
Bouldin de Broglie wavelength – Louis de Broglie de Bruijn sequences – Nicolaas Govert de Bruijn de Haas–van Alphen effect – Wander Johannes de Haas and
Scientific phenomena named after people
Scientific_phenomena_named_after_people
Existence of a line through two points
Melchior's proof showed that t 2 ( n ) ≥ 3 {\displaystyle t_{2}(n)\geq 3} . de Bruijn and Erdős (1948) raised the question of whether t 2 ( n ) {\displaystyle
Sylvester–Gallai_theorem
Molecule that carries genetic information
1038/nature04727. PMID 16710414. Anderson S, Bankier AT, Barrell BG, de Bruijn MH, Coulson AR, Drouin J, et al. (April 1981). "Sequence and organization
DNA
931–1090 Gilaki dynasty of northern Iran
XI, Fasc. 2. pp. 126–129. Rypka 1968, p. 146-147. Rypka 1968, p. 147. de Bruijn 2019, p. 13. Dabashi 2012, p. 78-79. Bosworth, C. E. (1968). "The Political
Ziyarid_dynasty
distinction between signs of i and −i is in some ways arbitrary, but a useful notational device. See imaginary unit for more information. Weisstein, Eric W. "Constant"
List of mathematical constants
List_of_mathematical_constants
tree construction algorithm. Velvet: a set of algorithms manipulating de Bruijn graphs for genomic sequence assembly Geohash: a public domain algorithm
List_of_algorithms
Graphs formed by a hypercube's edges and vertices
directed edge. Wikimedia Commons has media related to Hypercube graphs. de Bruijn graph Cube-connected cycles Fibonacci cube Folded cube graph Frankl–Rödl
Hypercube_graph
Commemorative coins of the Eurozone
'ART NOUVEAU'. At the far right are the initials of the designer Iris Bruijns located. As the Royal Dutch Mint will strike the coins, the mintmark of
2_euro_commemorative_coins
Algorithm in number theory
probability about a − a {\displaystyle a^{-a}} (an approximation to the Dickman–de Bruijn function), indicates that choosing too small a factor base is much worse
Dixon's_factorization_method
Gene whose sequence partially overlaps the reading frame of another gene
1003162. PMC 3744397. PMID 23966842. Anderson S, Bankier AT, Barrell BG, de Bruijn MH, Coulson AR, Drouin J, Eperon IC, Nierlich DP, Roe BA, Sanger F, Schreier
Overlapping_gene
Assignment of colors to edges of a graph
which every two color classes differ in size by at most one unit. The De Bruijn–Erdős theorem may be used to transfer many edge coloring properties of
Edge_coloring
Quantum analog of probabilistic automata
the Fubini–Study metric. The state transitions, transition matrices or de Bruijn graphs are represented by a collection of N × N {\displaystyle N\times
Quantum_finite_automaton
Geometric graph with unit edge lengths
distance graph formed from all points of the Euclidean plane. By the de Bruijn–Erdős theorem, which assumes the axiom of choice, this is equivalent to
Unit_distance_graph
Unsolved problem in extremal graph theory
Mellinger, Keith E.; Mubayi, Dhruv; Verstraëte, Jacques (2012), "The de Bruijn-Erdős Theorem for Hypergraphs", Des. Codes Cryptogr., 65 (3): 233–245
Zarankiewicz_problem
American motorsport season
Archived from the original on February 3, 2014. Retrieved October 22, 2011. de Bruijn, Wouter (November 29, 2005). "Road America returns to the 2006 Champcar
2006_Champ_Car_World_Series
reduction) DeWitt Bristol Brace DeWitt notation De Broglie–Bohm theory De Bruijn graph De Haas–van Alphen effect De Laval nozzle De Magnete De Sitter double
Index_of_physics_articles_(D)
Solution of a simplified form of an equation
(LG) or Wentzel–Kramers–Brillouin (WKB) approximation. White 2010, p. 2. de Bruijn 1981, pp. 187–189. Christensen 1996. White 2010, pp. 1–14. Fishaleck &
Method_of_dominant_balance
DE BRUIJN-NOTATION
DE BRUIJN-NOTATION
Girl/Female
Hindu, Indian, Tamil
God; Nature; Enjoy
Boy/Male
Indian, Modern
Good Performance; Good Person
Male
English
 Old French derogatory byname derived from the Old Occitan word brian, BRIAN means "maggot." Compare with another form of Brian.
Male
Irish
 Irish name derived from Celtic Brigonos, BRIAN means "high hill." Compare with another form of Brian.
Male
Ukrainian
, dwells near the weeds.
Surname or Lastname
Dutch
Dutch : from a personal name based on Middle Dutch bruun ‘brown’, or a nickname referring to the color of the hair or complexion. See also Braun.English : of uncertain origin. Reaney suggests that the name may simply reflect a pronunciation of French Brun.Altered spelling of Swiss Bruhin.
Boy/Male
Russian Ukrainian
Lives near the weeds.
Female
Welsh
Variant spelling of Welsh unisex Bryn, BRIN means "hill."
Boy/Male
German, Polish
Brown
Female
Irish
Irish name derived from the word Ãtu, ÃDE means "thirst."
Male
Irish
Variant spelling of Irish Brian, BRION means "high hill."
Boy/Male
Polish German
Brown (colour name).
Surname or Lastname
English
English : habitational name from a place in Somerset named Bruton, ‘settlement (Old English tūn) on the Brue river’. The river name is derived from a British element cognate with Welsh bryw ‘brisk’, ‘vigorous’.
Boy/Male
Shakespearean
King John' Hubert De Burgh.
Female
Finnish
Finnish name SÄDE means "ray of light."
Male
Dutch
, brown.
Female
French
French form of Old High German Adalhaid, ADÉLAÃDE means "noble sort."
Surname or Lastname
English (De Lisle) and French
English (De Lisle) and French : topographic and habitational name (see Lyle).
Boy/Male
Shakespearean
Love's Labours Lost' Don Adriano De Armado, fantastical Spaniard.
Boy/Male
Chinese
Virtue.
DE BRUIJN-NOTATION
DE BRUIJN-NOTATION
Biblical
nourishing
Boy/Male
Muslim/Islamic
Reward favour
Girl/Female
Gujarati, Hindu, Indian, Kannada
Bright Girl
Boy/Male
Hindu, Indian
Zodiac
Boy/Male
Tamil
Name of a sage
Biblical
desert
Boy/Male
Tamil
Victorious superior, Lord Ganesh
Boy/Male
Tamil
Shvetang | à®·à¯à®µà¯‡à®¤à®¾à®‚க
Fair complexioned
Girl/Female
British, English
Island of Linden Trees
Boy/Male
Welsh
Liar.
DE BRUIJN-NOTATION
DE BRUIJN-NOTATION
DE BRUIJN-NOTATION
DE BRUIJN-NOTATION
DE BRUIJN-NOTATION
n.
See Fleur-de-lis, 2.
n.
Short for Carte de visite.
pl.
of Auto-de-fe
pl.
of Aid-de-camp
n.
The manner or style of execution of an engraver; as, a soft burin; a brilliant burin.
n.
A heavy silk with a dull finish; as, gros de Naples; gros de Tours.
v. t.
To injure, as by a blow or collision, without laceration; to contuse; as, to bruise one's finger with a hammer; to bruise the bark of a tree with a stone; to bruise an apple by letting it fall.
pl.
of Tete-de-pont
pl.
of Cul-de-sac
pl.
of Cheval-de-frise
pl.
of Trou-de-loup
n.
The iris. See Flower-de-luce.
n.
The cobra de capello.
pl.
of Fleur-de-lis
pl.
of Felo-de-se
n.
See Trou-de-loup.
pl.
of Carte de visite