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...

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...

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

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...

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...

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

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

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

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...

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

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...

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...

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

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

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...

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

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

In mathematics, a homogeneous space is, very informally, a space that looks the same everywhere, as you move through it, with movement given by the action...

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...

In set theory a serial relation is a homogeneous relation expressing the connection of an element of a sequence to the following element. The successor...

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...

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...

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 (...

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...

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...

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