In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian...

Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation Homogeneous relation Reflexive relation Serial...

each relation has a place in the lattice of subsets of X × Y . {\displaystyle X\times Y.} A binary relation is called a homogeneous relation when X...

a < c; and if x = y and y = z then x = z. A homogeneous relation R on the set X is a transitive relation if, for all a, b, c ∈ X, if a R b and b R c,...

heterogeneous relation between set of points and lines Order theory, investigates properties of order relations Relation algebra called "homogeneous binary relation...

Y ≠ ∅ . {\displaystyle Y\neq \emptyset .} : 57  Serial relation — a total homogeneous relation If Y = ∅ ≠ X , {\displaystyle Y=\emptyset \neq X,} then...

algebra, homogeneous polynomials have the same number of factors of a given kind. In the study of binary relations, a homogeneous relation R is on a...

which every pair is comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially...

strongly connected as defined above. Let R {\displaystyle R} be a homogeneous relation. The following are equivalent: R {\displaystyle R} is strongly connected;...

A symmetric relation is a type of binary relation. Formally, a binary relation R over a set X is symmetric if: ∀ a , b ∈ X ( a R b ⇔ b R a ) , {\displaystyle...

reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to...

mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments in...

refer to R as an n-ary relation over X, called a homogeneous relation. Without this restriction, R is called a heterogeneous relation. When any of Xi is empty...

property this "incomparability relation" needs in order to be an equivalence relation. Define also an induced homogeneous relation ≲ {\displaystyle \,\lesssim...

relation of an antichain is just the identity relation. Approximates relation. See way-below relation. Antisymmetric relation. A homogeneous relation...

In mathematics, an asymmetric relation is a binary relation R {\displaystyle R} on a set X {\displaystyle X} where for all a , b ∈ X , {\displaystyle...

In mathematics, a binary relation R is called well-founded (or wellfounded or foundational) on a set or, more generally, a class X if every non-empty subset...

In mathematics, a binary relation R {\displaystyle R} on a set X {\displaystyle X} is antisymmetric if there is no pair of distinct elements of X {\displaystyle...

by the Fibonacci numbers is the canonical example of a homogeneous linear recurrence relation with constant coefficients (see below). The Fibonacci sequence...

which any two elements are comparable. That is, a total order is a binary relation ≤ {\displaystyle \leq } on some set X {\displaystyle X} , which satisfies...

Homogeneous linear transformation Homogeneous model in model theory Homogeneous polynomial Homogeneous relation: binary relation on a set Homogeneous...

simple graph permitting loops G is a homogeneous relation ~ on the vertices of G that is called the adjacency relation of G. Specifically, for each edge...

mathematics, the transitive closure R+ of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive. For...

above relation is true for infinitely many λ {\displaystyle \lambda } then the polynomial is homogeneous of degree d. In particular, if P is homogeneous then...

is both right-invertible and left-invertible. For an invertible homogeneous relation R , {\displaystyle R,} all right and left inverses coincide; this...

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total ordering on S with the property that every non-empty subset...

equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) is a homogeneous binary relation that is...

differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written f (...

mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest...

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are...