en.unionpedia.org

Covering relation, the Glossary

In mathematics, especially order theory, the covering relation of a partially ordered set is the binary relation which holds between comparable elements that are immediate neighbours.^[1]

24 relations: Associahedron, Binary relation, Boolean algebra (structure), Cambridge University Press, Comparability, Dense order, Distributive lattice, Hasse diagram, Integer partition, Mathematics, Median graph, N-skeleton, Order theory, Partially ordered set, Power set, Rational number, Real number, Subset, Tamari lattice, The Art of Computer Programming, Total order, Transitive reduction, Young tableau, Young's lattice.
Binary relations

Associahedron

In mathematics, an associahedron is an -dimensional convex polytope in which each vertex corresponds to a way of correctly inserting opening and closing parentheses in a string of letters, and the edges correspond to single application of the associativity rule.

See Covering relation and Associahedron

Binary relation

In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. Covering relation and binary relation are binary relations.

See Covering relation and Binary relation

Boolean algebra (structure)

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.

See Covering relation and Boolean algebra (structure)

Cambridge University Press

Cambridge University Press is the university press of the University of Cambridge.

See Covering relation and Cambridge University Press

Comparability

In mathematics, two elements x and y of a set P are said to be comparable with respect to a binary relation ≤ if at least one of x ≤ y or y ≤ x is true. Covering relation and Comparability are binary relations and order theory.

See Covering relation and Comparability

Dense order

In mathematics, a partial order or total order X is said to be dense if, for all x and y in X for which x, there is a z in X such that x. That is, for any two elements, one less than the other, there is another element between them. Covering relation and dense order are order theory.

See Covering relation and Dense order

Distributive lattice

In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other.

See Covering relation and Distributive lattice

Hasse diagram

In order theory, a Hasse diagram is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction. Covering relation and Hasse diagram are order theory.

See Covering relation and Hasse diagram

Integer partition

In number theory and combinatorics, a partition of a non-negative integer, also called an integer partition, is a way of writing as a sum of positive integers.

See Covering relation and Integer partition

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Covering relation and Mathematics

In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest paths between each pair of a, b, and c. The concept of median graphs has long been studied, for instance by or (more explicitly) by, but the first paper to call them "median graphs" appears to be.

See Covering relation and Median graph

N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space presented as a simplicial complex (resp. CW complex) refers to the subspace that is the union of the simplices of (resp. cells of) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.

See Covering relation and N-skeleton

Order theory

Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations.

See Covering relation and Order theory

Partially ordered set

In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. Covering relation and Partially ordered set are binary relations and order theory.

See Covering relation and Partially ordered set

Power set

In mathematics, the power set (or powerset) of a set is the set of all subsets of, including the empty set and itself.

See Covering relation and Power set

Rational number

In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

See Covering relation and Rational number

Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

See Covering relation and Real number

Subset

In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).

See Covering relation and Subset

Tamari lattice

In mathematics, a Tamari lattice, introduced by, is a partially ordered set in which the elements consist of different ways of grouping a sequence of objects into pairs using parentheses; for instance, for a sequence of four objects abcd, the five possible groupings are ((ab)c)d, (ab)(cd), (a(bc))d, a((bc)d), and a(b(cd)).

See Covering relation and Tamari lattice

The Art of Computer Programming

The Art of Computer Programming (TAOCP) is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis.

See Covering relation and The Art of Computer Programming

Total order

In mathematics, a total order or linear order is a partial order in which any two elements are comparable. Covering relation and total order are order theory.

See Covering relation and Total order

Transitive reduction

In the mathematical field of graph theory, a transitive reduction of a directed graph is another directed graph with the same vertices and as few edges as possible, such that for all pairs of vertices, a (directed) path from to in exists if and only if such a path exists in the reduction.

See Covering relation and Transitive reduction