In mathematics, an incidence poset or incidence order is a type of partially ordered set that represents the incidence relation between vertices and edges of an undirected graph. The incidence poset of a graph G has an element for each vertex or edge in G; in this poset, there is an order relation x ≤ y if and only if either x = y or x is a vertex, y is an edge, and x is an endpoint of y.
In mathematics, an incidenceposet or incidence order is a type of partially ordered set that represents the incidence relation between vertices and edges...
dimension of its incidenceposet is at most three (Schnyder 1989). For a complete graph on n vertices, the order dimension of the incidenceposet is Θ ( log...
~x~\leq ~b}f(a,x)g(x,b).} An incidence algebra is finite-dimensional if and only if the underlying poset is finite. An incidence algebra is analogous to a...
that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is an ordered pair P = ( X , ≤ ) {\displaystyle P=(X,\leq )}...
relation <. Formally, P (with <) will be a (strict) partially ordered set, or poset. Just as the number zero is necessary in mathematics, so also every set...
z)g(z,y).} There is also a definition of incidence coalgebra. In theoretical physics a locally finite poset is also called a causal set and has been used...
subset X of a poset P that is a directed lower set. The dual notion is called filter. Incidence algebra. The incidence algebra of a poset is the associative...
of posets exist. For example, a poset is locally finite if every closed interval [a, b] in it is finite. Locally finite posets give rise to incidence algebras...
function of a Lie group Zeta function of an incidence algebra, a function that maps every interval of a poset to the constant value 1. Despite not resembling...
as trigonometric coalgebra. For a locally finite poset P with set of intervals J, define the incidence coalgebra C with J as basis. The comultiplication...
partially ordered set (poset) of elements, such that incidences, or connections, between elements of the set correspond to incidences between elements (faces...
Euler characteristic of such a poset is defined as the integer μ(0,1), where μ is the Möbius function in that poset'sincidence algebra. This can be further...
eventually to the theory of abstract polytopes as partially ordered sets, or posets, of such elements. Peter McMullen and Egon Schulte published their book...
We can recover the poset S from the nerve NS and the category C from the nerve NC; in this sense simplicial sets generalize posets and categories. Another...
entities cannot each be a part of the other (antisymmetry), thus forming a poset. A variant of this axiomatization denies that anything is ever part of itself...
special case of the convolution multiplication for the incidence algebra of a poset, in this case the poset of positive integers ordered by divisibility. Arithmetic...
polytope is a partially ordered set (poset) of elements whose partial ordering obeys certain rules of incidence (connectivity) and ranking. The elements...
formalism of incidence algebras, difference operators and other Möbius inversion can be represented by convolution with a function on the poset, called the...
ground has one entry. Multiorders are a generalization of partial orders (posets), and were first introduced (in passing) by Tom Leinster. There is a multicategory...
1016/0095-8956(86)90043-2. MR 0859310. Zbl 0605.05024. Jung, H. A. (1978). "On a class of posets and the corresponding comparability graphs". Journal of Combinatorial Theory...
Domain theory a branch that studies special kinds of partially ordered sets (posets) commonly called domains. Donaldson theory the study of smooth 4-manifolds...
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