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Copy of a directed graph with redundant edges removed
In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges
Transitive_reduction
Directed graph with no directed cycles
contains a longer directed path from u to v. Like the transitive closure, the transitive reduction is uniquely defined for DAGs. In contrast, for a directed
Directed_acyclic_graph
Smallest transitive relation containing a given binary relation
p. 337). We have R+ = R if, and only if, R itself is transitive. Conversely, transitive reduction reduces a minimal relation S from a given relation R
Transitive_closure
Type of binary relation
In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates
Transitive_relation
Visual depiction of a partially ordered set
a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set ( S , ≤ ) {\displaystyle
Hasse_diagram
Transformations induced by a mathematical group
{\displaystyle g\cdot x=y} . The action is simply transitive (or sharply transitive, or regular) if it is both transitive and free. This means that given x , y ∈
Group_action
Node ordering for directed acyclic graphs
for which x ≤ y. An alternative way of doing this is to use the transitive reduction of the partial ordering; in general, this produces DAGs with fewer
Topological_sorting
Method for partitioning partial orders into levels
directed consistently downwards. For a partial ordering given by its transitive reduction (covering relation), the Coffman–Graham algorithm can be implemented
Coffman–Graham_algorithm
Visual representation of a mathematical relationship
partially ordered set, forming a drawing of the partial order's transitive reduction. Concretely, one represents each element of the set as a vertex on
Mathematical_diagram
Directed graph representing dependencies
{\displaystyle G=(S,T)} with T ⊆ R {\displaystyle T\subseteq R} the transitive reduction of R. For example, assume a simple calculator. This calculator supports
Dependency_graph
A transitive reduction of a graph is a minimal graph having the same transitive closure; directed acyclic graphs have a unique transitive reduction. A
Glossary_of_graph_theory
Mathematical set with an ordering
node and each element of < {\displaystyle <} to be an edge. The transitive reduction of this DAG is then the Hasse diagram. Similarly this process can
Partially_ordered_set
Mathematical-logic system based on functions
the number of β-reduction steps taken by normal order reduction to reduce a term is a reasonable time cost model, that is, the reduction can be simulated
Lambda_calculus
Pattern relating to the subject and object of verbs
intransitive verb behaves like the object of a transitive verb, and differently from the subject of a transitive verb. All known ergative languages show ergativity
Ergative–absolutive_alignment
Mathematical relation inside orderings
a partially ordered set is finite, its covering relation is the transitive reduction of the partial order relation. Such partially ordered sets are therefore
Covering_relation
Whether one vertex can be reached from another in a graph
defined in this way, for instance as the reachability relation of its transitive reduction. A noteworthy consequence of this is that since partial orders are
Reachability
Five sporadic simple groups
M23 and M24 introduced by Émile Mathieu (1861, 1873). They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objects. They are the first
Mathieu_group
Method of comparing problems by transforming one into another in computability theory
natural numbers that is Reflexive: Every set is reducible to itself. Transitive: If a set A {\displaystyle A} is reducible to a set B {\displaystyle B}
Reduction (computability theory)
Reduction_(computability_theory)
Type of graph in mathematics
partial order. Conversely, in a diamond-free partial order, the transitive reduction identifies a directed acyclic graph in which the subgraph reachable
Multitree
Glossary of terms used in branch of mathematics
a finite partially ordered set, in the form of a drawing of its transitive reduction. Homogeneous relation. A homogeneous relation on a set X {\displaystyle
Glossary_of_order_theory
Formal system for transcribing expressions into equivalent terms
}}} is the transitive closure of → {\displaystyle \rightarrow } . → ∗ {\displaystyle {\stackrel {*}{\rightarrow }}} is the reflexive transitive closure of
Abstract_rewriting_system
Smallest complete lattice containing a partial order
to this version of the Dedekind–MacNeille completion problem. The transitive reduction or covering graph of the Dedekind–MacNeille completion describes
Dedekind–MacNeille_completion
Type of computational algorithm
{\displaystyle g\circ f} . This allows the concept of logspace reduction to be transitive. Given two logspace transducers, their composition is still a
Log-space_reduction
Transformation of one computational problem to another
complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to
Reduction_(complexity)
Category of formal programming language semantics
symmetric-transitive-reflexive closure—is a sound reasoning principle for these languages. However, in practice, most applications of reduction semantics
Operational_semantics
Replacing subterm in a formula with another term
ARS. → ∗ {\displaystyle {\overset {*}{\rightarrow }}} is the reflexive transitive closure of → {\displaystyle \rightarrow } . ↔ {\displaystyle \leftrightarrow
Rewriting
Type of Turing reduction
and computational complexity theory, a many-one reduction (also called mapping reduction) is a reduction that converts instances of one decision problem
Many-one_reduction
subset of a reduction ordering. Conversely, for every terminating term rewriting system, the transitive closure of (::=) is a reduction ordering, which
Rewrite_order
Directed graph describing citations in documents
James R Clough; Jamie Gollings; Tamar V Loach; Tim S Evans (2015). "Transitive reduction of citation networks". Journal of Complex Networks. 3 (2): 189–203
Citation_graph
Concept in computability theory
In computability theory, a Turing reduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle B} is an oracle machine
Turing_reduction
Reflexive and transitive binary relation
a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest that preorders are almost partial
Preorder
Binary relation that relates every element to itself
property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations
Reflexive_relation
Type of group in abstract algebra
inclusion map S5 → S6 as a transitive subgroup; the obvious inclusion map Sn → Sn+1 fixes a point and thus is not transitive. This yields the outer automorphism
Symmetric_group
Concept in mathematics
In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a
Reductive_group
this way have been called vertex series parallel graphs, and their transitive reductions (the graphs of the covering relations of the partial order) are
Series-parallel_partial_order
Planar directed acyclic graph
forms a two-dimensional complete lattice, whose Hasse diagram is the transitive reduction of the given graph. Conversely, the Hasse diagram of every two-dimensional
St-planar_graph
Type of geometry
program. More specifically, it is a homogeneous space X together with a transitive action on X by a Lie group G, which acts as the symmetry group of the
Klein_geometry
Binary relation over a set and itself
containing R. Reflexive reduction, R≠ Defined as R≠ = R \ {(x, x) | x ∈ X} or the largest irreflexive relation over X contained in R. Transitive closure, R+ Defined
Homogeneous_relation
Missouri Valley Siouan language of Montana, US
stative verbs, active transitive verbs, and from active intransitive verbs. ii – 'instrumental nominalizer': Derived from active transitive and intransitive
Crow_language
Number and type of arguments controlled by a linguistic predicate
Valency is related, though not identical, to subcategorization and transitivity, which count only object arguments – valency counts all arguments, including
Valency_(linguistics)
Theorem in theoretical computer science
two lambda expressions. If β-reduction is denoted by → β {\displaystyle \rightarrow _{\beta }} and its reflexive, transitive closure by ↠ β {\displaystyle
Church–Rosser_theorem
Cariban language of Brazil, Suriname and Guyana
the subject of a transitive clause is marked with the postposition _:ja; the subjects of intransitive clauses and objects of transitive sentences are both
Tiriyó_language
Type of grammatical voice
reflexive and reciprocal constructions, the unifying feature being a reduction in transitivity. Indeed, it is more common for languages to have a coincidence
Antipassive_voice
Relation specifying a rewrite for each object, compatible with a reduction relation
{\overset {+}{\to }}} , where → + {\displaystyle {\overset {+}{\to }}} is the transitive closure of → {\displaystyle \to } (but not the reflexive closure). In
Reduction_strategy
Mapping a graph onto itself without changing edge-vertex connectivity
graph that is edge-transitive but not vertex-transitive. A half-transitive graph is a graph that is vertex-transitive and edge-transitive but not symmetric
Graph_automorphism
Language of the Yupik family
grammatical case (the absolutive) as the objects of transitive verbs, while the subjects of transitive verbs have a different case (the ergative). For example
Central_Alaskan_Yupʼik
Order whose elements are all comparable
and b ≤ c {\displaystyle b\leq c} then a ≤ c {\displaystyle a\leq c} (transitive). If a ≤ b {\displaystyle a\leq b} and b ≤ a {\displaystyle b\leq a} then
Total_order
Any individual whose preferences satisfy four axioms has a utility function
reflexivity.[clarification needed] Transitivity assumes that preferences are consistent across any three options: Axiom 2 (Transitivity) If L ⪰ M {\displaystyle
Von Neumann–Morgenstern utility theorem
Von_Neumann–Morgenstern_utility_theorem
Concept of sentence structure in linguistics
intransitive verbs are treated like subjects of transitive verbs, and are distinguished from objects of transitive verbs in basic clause constructions. Nominative–accusative
Nominative–accusative alignment
Nominative–accusative_alignment
Sporadic simple group
groups and was introduced by Mathieu (1861, 1873). It is a sharply 5-transitive permutation group on 12 objects. Burgoyne & Fong (1968) showed that the
Mathieu_group_M12
Munda language of South Asia
Medio-passive voice. Transitive roots, transitive-intransitive roots, and causative stems will take -ok to derive passive stems. In the transitive-intransitive
Santali_language
Group whose operation is composition of permutations
permutations of {1, 2, 3, 4} is not transitive (no group element takes 1 to 3) but the group of symmetries of a square is transitive on the vertices. A permutation
Permutation_group
Mayan language of Chiapas, Mexico
classifiers. First, some transitive roots reduce valence by infixing -j- into the root. This process is accompanied by a reduction of the number of core
Chʼol_language
Property of rewriting systems in mathematics
Since a sequence of reduction sequences is again a reduction sequence (or, equivalently, since forming the reflexive-transitive closure is idempotent)
Confluence (abstract rewriting)
Confluence_(abstract_rewriting)
Class of computational complexity
logic with the addition of a transitive closure operator. A full transitive closure is not needed; a commutative transitive closure and even weaker forms
PSPACE
Language family of the Arctic and sub-Arctic
intransitive verbs and objects of transitive verbs are marked with the absolutive case, while subjects of transitive verbs are marked with the ergative
Eskaleut_languages
Verb whose direct object is the same as its subject
return.REFL+NPST When will you return? The same valence-reduction process occurs for the transitive wagil 'cut' Gaari NEG wagi-iyi cut-REFL+IMP Gaari wagi-iyi
Reflexive_verb
Roof of a building that is designed to provide temporary water storage
utilize a novel passive blue roof tray design which relies on the lateral transitivity of non-woven filter fabric for drawdown control in a full scale pilot
Blue_roof
Language of the ancient Urartu, now the Eastern Anatolia region
and the object of a transitive verb are expressed identically, with the so-called absolutive case, whereas the subject of a transitive verb is expressed
Urartian_language
Vocabulary of a language or branch of knowledge
language's rules. For example, the suffix "-able" is usually only added to transitive verbs, as in "readable" but not "cryable". A compound word is a lexeme
Lexicon
Endangered Salishan language of the US
transitivizer used in the predicate, those occurring with m primarily occur with the causative transitivizer -st(u)- while all other transitivizers take
Coeur_d'Alene_language
Fiber bundle whose fibers are group torsors
to the base space X {\displaystyle X} . Because the action is free and transitive, the fibers have the structure of G-torsors. A G {\displaystyle G} -torsor
Principal_bundle
American mathematician (1936–2024)
Cartan's papers from the early 1900s on the classification of the simple transitive infinite Lie pseudogroups, and of relating Cartan's results to recent
Shlomo_Sternberg
Concept in mathematics
In mathematics, a Frobenius group is a transitive permutation group on a finite set, such that no non-trivial element fixes more than one point and some
Frobenius_group
Order by which an agent ranks alternatives based on their utility
option that maximizes their self-interest. But preferences are not always transitive, both because real humans are far from always being rational and because
Preference_(economics)
Graph that can be embedded in the plane
ISBN 978-3-540-12687-4. Halldórsson, M.; Kitaev, S.; Pyatkin., A. (2016), "Semi-transitive orientations and word-representable graphs" (PDF), Discr. Appl. Math.
Planar_graph
acyclic graph Directed graph Distance regular graph Distance-transitive graph Edge-transitive graph Interval graph Interval graph, improper Interval graph
List_of_graph_theory_topics
Reduction of data redundancy
the Book and Price tables conform to 2NF. The Book table still has a transitive functional dependency ({Author Nationality} is dependent on {Author},
Database_normalization
Ways how entities stand to each other
propositions while causal relations connect concrete events. Symmetric, transitive, and reflexive relations are distinguished by their structural features
Relation_(philosophy)
intransitive verbs and Direct Object of transitive verbs. Ergative (Erg): Marks the Subject (Agent) of transitive verbs. Oblique (Obl): Marks Indirect Objects
Adyghe_verbs
West Germanic language
or direct object of a transitive verb), and of the Old English dative case (for a recipient or indirect object of a transitive verb). The subjective is
English_language
Indigenous language of South America
an active-stative language. In other words, Guarani consists of active transitive verbs as well as both active and stative intransitive verbs. To indicate
Guarani_language
Grammatical form
exceptional case-marking. As shown in the above examples, the object of the transitive verb want and the preposition for allude to their respective pronouns'
Infinitive
Sporadic simple group
sporadic groups and was introduced by Mathieu (1861, 1873). It is a 5-transitive permutation group on 24 objects. The Schur multiplier and the outer automorphism
Mathieu_group_M24
Construction in group theory
sharply 3-transitive (faithful and 3-transitive), so the map is one-to-one and has image a 3-transitive subgroup. Thus the image is a 3-transitive subgroup
Projective_linear_group
Logical quantifier
5. {\displaystyle a+2=5{\text{ and }}b+2=5.} Then since equality is a transitive relation, a + 2 = b + 2. {\displaystyle a+2=b+2.} Subtracting 2 from both
Uniqueness_quantification
Reconstructed ancestor of the Circassian languages
action) While most transitive verbs in Circassian are inherently dynamic, the verb Iыгъын (to hold) is a unique bivalent transitive static verb. In its
Proto-Circassian_language
Earliest stage of the German language
showed case and gender endings—for intransitive verbs the nominative, for transitive verbs the accusative. For example: After thie thö argangana warun ahtu
Old_High_German
Set theory concept
{\displaystyle X} is a preorder ≤ {\displaystyle \leq } on X {\displaystyle X} (a transitive and reflexive relation on X {\displaystyle X} ) that is strongly connected
Prewellordering
People who have acquired Esperanto as one of their native languages
rul 'roll'. Without the suffix -iĝos, however, the meaning would be a transitive 'I will roll you over'.) Adverbs from verbs Ege halte, ege paŭze, ege
Native_Esperanto_speakers
Computation modulo a fixed integer
a ≡ a (mod m) Symmetry: a ≡ b (mod m) if and only if b ≡ a (mod m). Transitivity: If a ≡ b (mod m) and b ≡ c (mod m), then a ≡ c (mod m) If a1 ≡ b1 (mod
Modular_arithmetic
Sporadic simple group
and the outer automorphism group are both trivial. M11 is a sharply 4-transitive permutation group on 11 objects. It admits many generating sets of permutations
Mathieu_group_M11
Arabic-language term for a truce or armistice
Ibn Manzur defined it as: "hadana: he grew quiet. hadina: he quieted (transitive or intransitive). haadana: he made peace with. The noun from each of these
Hudna
Samoyedic language
constraint on word order. Below are examples of the basic word order for a transitive and intransitive sentence. məy°mpə-da cheerful-IMPF.PART Wera Wera Maša-m
Tundra_Nenets_language
English philosopher (1944–2014)
Stressing the need to retain both the subjective epistemological, or 'transitive', side of knowledge and the objective ontological, or 'intransitive',
Roy_Bhaskar
Generalization of graph theory
hypergraphs; Hall-type theorems for hypergraphs. In directed hypergraphs: transitive closure, and shortest path problems. Although hypergraphs are more difficult
Hypergraph
East Slavic language
Some studies found that in modern Russian vernacular the chance that a transitive Russian sentence is judged "SVO" fluctuates between 40% and 45%; the rest
Russian_language
require the use of the reflexive pronoun, appropriate to the subject. Some transitive verbs can take on a reflexive meaning, such as lavar (to wash) and lavarse
Personal_pronouns_in_Spanish
include the development of a Descriptive Scenario, a Normative Scenario and Transitive Scenario. Essentially, the Descriptive Scenario "describe[s] the situation
Earth systems engineering and management
Earth_systems_engineering_and_management
Grammatical rules of the modern-day Hebrew language
/paˈtaħ//נִפְתַּח /nifˈtaħ/ (to open, transitive/intransitive) and גָּמַר /ɡaˈmar//נִגְמַר /niɡˈmar/ (to end, transitive/intransitive). Other relationships
Modern_Hebrew_grammar
Tupian language of Brazil
forgive) (incl.) pe poasem (you moan) (pl.) i pytu (they breathe) Objects of transitive verbs in Old Tupi may come in many positions relative to the verb: either
Tupi_language
Extinct language family
suffixes of the head. In verbs, the type of valency, intransitive vs transitive, is signalled by a special suffix, the so-called "class marker". The complex
Hurro-Urartian_languages
Network that allows computers to share resources and communicate with each other
to only a small increase in the network throughput or to a potential reduction in network throughput. Network protocols that use aggressive retransmissions
Computer_network
Concept in group theory
of G on the cosets of B is doubly transitive. So (B, N) pairs of rank 1 are more or less the same as doubly transitive actions on sets with more than 2
(B,_N)_pair
In mathematics and theoretical computer science, a pattern is an unavoidable pattern if it is unavoidable on any finite alphabet. Like a word, a pattern
Unavoidable_pattern
Argument in philosophy of mathematics
insofar as ∅ is not an element of {{∅}}. Thus, in terms of failing the transitivity of identity, the search for true identity statements similarly fails
Benacerraf's identification problem
Benacerraf's_identification_problem
Maximal subgraph whose vertices can reach each other
These graphs may be produced as the transitive closures of arbitrary undirected graphs, for which finding the transitive closure is an equivalent formulation
Component_(graph_theory)
Endangered language spoken in Canada and Alaska
possessive pronoun before relational nouns and prepositions, and cliticized to transitive verbs an is the object pronoun, while -ang is the bound possessive pronoun
Haida_language
Total order in computer science
ordering to another one, and satisfying the following properties: If (>) is transitive, then so is O(>). If (>) is irreflexive, then so is O(>). If s > t, then
Path ordering (term rewriting)
Path_ordering_(term_rewriting)
Disparity filter is a network reduction algorithm (a.k.a. graph sparsification algorithm ) to extract the backbone structure of undirected weighted network
Disparity filter algorithm of weighted network
Disparity_filter_algorithm_of_weighted_network
TRANSITIVE REDUCTION
TRANSITIVE REDUCTION
Boy/Male
Tamil
Transition
Surname or Lastname
English and Scottish
English and Scottish : nickname for a mild and gentle man, from Middle English do ‘doe’ (Old English dÄ).English (of Norman origin) : habitational name (Old French d’Eu) for someone from Eu in Seine-Maritime, France. The place name is either a dramatic reduction of Latin Augusta ‘(city of) Augustus’, or else derives from the Germanic element auwa ‘water meadow’, ‘island’.
Boy/Male
Hindu
Transition
Surname or Lastname
English and Scottish
English and Scottish : topographic name, a variant of Sell 1.English and Scottish : occupational name for a saddler, from Anglo-Norman French seller (Old French sellier, Latin sellarius, a derivative of sella ‘seat’, ‘saddle’).English and Scottish : metonymic occupational name for someone employed in the cellars of a great house or monastery, from Anglo-Norman French celler ‘cellar’ (Old French cellier), or a reduction of the Middle English agent derivative cellerer.English and Scottish : occupational name for a tradesman or merchant, from an agent derivative of Middle English sell(en) ‘to sell’ (Old English sellan ‘to hand over, deliver’).German : probably a habitational name from a place named Sella near Hoyerswerda.
Boy/Male
Hindu, Indian
Age of Transition; New Age
TRANSITIVE REDUCTION
TRANSITIVE REDUCTION
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from Birdsall, near Malton, in North Yorkshire, so named with the genitive case of the Old English byname Bridd meaning ‘bird’ + Old English halh ‘nook’, ‘recess’.
Girl/Female
Hindu, Indian, Sanskrit, Traditional
Most Loved One
Boy/Male
Indian, Punjabi, Sikh
Light for All
Boy/Male
American, Australian, British, English
Old and Wise Ruler
Boy/Male
Hebrew
My father is alive.
Boy/Male
Irish American Welsh
Loyal.
Boy/Male
Hindu
Orderly
Boy/Male
Tamil
Aanantya | ஆநஂதà¯à®¯à®¾
Divine
Male
Egyptian
, a title of the god Horus.
Boy/Male
American, Anglo, Australian, British, English, German, Shakespearean, Teutonic
Divine Ruler
TRANSITIVE REDUCTION
TRANSITIVE REDUCTION
TRANSITIVE REDUCTION
TRANSITIVE REDUCTION
TRANSITIVE REDUCTION
a.
Of or pertaining to transition; involving or denoting transition; as, transitional changes; transitional stage.
n.
A direct or indirect passing from one key to another; a modulation.
n.
Change from one form to another.
v. t.
To require to be in a particular case; as, a transitive verb governs a noun in the objective case; or to require (a particular case); as, a transitive verb governs the objective case.
a.
Not passing farther; kept; detained.
a.
Effected by transference of signification.
a.
Transmitted or transmissible from father to son, or from age, by oral communication; traditional.
n.
A passing from one subject to another.
a.
Intransitive; as, a neuter verb.
n.
A transition from one subject to another.
n.
Passage from one place or state to another; charge; as, the transition of the weather from hot to cold.
adv.
Without an object following; in the manner of an intransitive verb.
a.
Passing over to an object; expressing an action which is not limited to the agent or subject, but which requires an object to complete the sense; as, a transitive verb, for example, he holds the book.
n.
Transition.
a.
tropical; figurative; as, a translative sense.
a.
Having the power of making a transit, or passage.
n.
An intransitive verb.
a.
Applied to verbs which assert that the subject acts upon or affects something else; transitive.
a.
Not transitive; not passing over to an object; expressing an action or state that is limited to the agent or subject, or, in other words, an action which does not require an object to complete the sense; as, an intransitive verb, e. g., the bird flies; the dog runs.