an Eulerian poset is a graded poset in which every nontrivial interval has the same number of elements of even rank as of odd rank. An Eulerian poset which...

h-vector, which is defined for an arbitrary ranked poset, and proved that for the class of Eulerian posets, the Dehn–Sommerville equations continue to hold...

mathematics, in the branch of combinatorics, a graded poset is a partially-ordered set (poset) P equipped with a rank function ρ from P to the set N...

that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is an ordered pair P = ( X , ≤ ) {\displaystyle P=(X,\leq )}...

groups act transitively on the set of flags of the polytope. Eulerian poset Graded poset Regular polytope McMullen & Schulte 2002, p. 31 McMullen & Schulte...

sets is open. Algebraic poset. A poset is algebraic if it has a base of compact elements. Antichain. An antichain is a poset in which no two elements...

to mean strong antichain, a subset such that there is no element of the poset smaller than two distinct elements of the antichain.) A maximal antichain...

(transitivity). A set with a partial order on it is called a partially ordered set, poset, or just ordered set if the intended meaning is clear. By checking these...

partially ordered set, or as an algebraic structure. A partially ordered set (poset) ( L , ≤ ) {\displaystyle (L,\leq )} is called a lattice if it is both a...

189.2.4. S2CID 119158401. Stanley, Richard P. (1994). "A survey of Eulerian posets". In Bisztriczky, T.; McMullen, P.; Schneider, R.; Weiss, A. Ivić...

introducing Zeta polynomials, for explicitly defining Eulerian posets, developing the theory of binomial posets along with Rota and Peter Doubilet, and more....

graded posets with unique minimal and maximal elements, preserving the property that the posets are Eulerian. The star product of two graded posets ( P ...

order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring...

existence of certain infima or suprema of a given partially ordered set (poset). The most familiar example is the completeness of the real numbers. A special...

a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially...

filter or order filter is a special subset of a partially ordered set (poset), describing "large" or "eventual" elements. Filters appear in order and...

)-\ell (\pi )}} , and thus this poset is Eulerian, meaning its Möbius function is produced by the rank function on the poset. The Bruhat graph is the vertex-edge...

generated from a given poset used in place of the set of generators considered above, then one speaks of a completion of the poset. The definition of the...

Ko-free Go Ladder capturing in Go Gomoku Hex Konane Lemmings Node Kayles Poset Game Reversi River Crossing Rush Hour Finding optimal play in Mahjong solitaire...

sets are also said to be duals if they are dually isomorphic, i.e. if one poset is order isomorphic to the dual of the other. The importance of this simple...

Dolores-Cuenca, Eric; Mendoza-Cortes, Jose L. (2022). "A poset version of Ramanujan results on Eulerian numbers and zeta values". arXiv:2205.05208v3 [math.CO]...

-complete proper filter on the set κ {\displaystyle \kappa } ; that is, on the poset ( ℘ ( κ ) , ⊆ ) {\displaystyle (\wp (\kappa ),\subseteq )} . If κ {\displaystyle...

linear time, if such a diagram exists. In particular, if the input poset is a graded poset, it is possible to determine in linear time whether there is a...

in terms of category theory. Formally, given two partially ordered sets (posets) ( S , ≤ ) {\displaystyle (S,\leq )} and ( T , ⪯ ) {\displaystyle (T,\preceq...

Willigenburg, Stephanie (25 June 2003), "Peak quasisymmetric functions and Eulerian enumeration", Advances in Mathematics, 176 (2): 248–276, arXiv:0706.3486...

Stanley; his dissertation was titled Permutation Statistics of Indexed and Poset Permutations. Einar moved to Gothenburg, Sweden in 1990, while still a graduate...

three order relations a ≤ b ≥ c ≤ d is an example of a fence or zigzag poset; its Hasse diagram has the shape of the capital letter "N". It is not series-parallel...

Hausdorff maximal principle. Indeed, let P {\displaystyle P} be a nonempty poset and X : = { C ⊆ P : C   is a chain } {\displaystyle X\mathrel {\mathop {:}...

sets ("posets") is reflexive: every poset is cofinal in itself. It is also transitive: if B {\displaystyle B} is a cofinal subset of a poset A , {\displaystyle...

Distributive Join and meet Reflexive Partial order Chain-complete Graded Eulerian Strict Prefix order Preorder Total Semilattice Semiorder Symmetric Total...