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...

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

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...

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...

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

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...

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

(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...

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

S2CID 38115497. Ganapathy, Jayanthi (1992). "Maximal Elements and Upper Bounds in Posets". Pi Mu Epsilon Journal. 9 (7): 462–464. ISSN 0031-952X. JSTOR 24340068...

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...

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...

)-\ell (\pi )}} , and thus this poset is Eulerian, meaning its Möbius function is produced by the rank function on the poset. Kazhdan–Lusztig polynomial Björner...

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...

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...

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

been studied; see map of lattices for a list. Partially ordered sets (or posets), orderings in which some pairs are comparable and others might not be Preorders...

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

37–46, doi:10.1016/0012-365X(83)90019-5. Jung, H. A. (1978), "On a class of posets and the corresponding comparability graphs", Journal of Combinatorial Theory...

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...

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...

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

set. If the considered partially ordered set (poset) has binary suprema (a.k.a. joins), as do the posets within this article, then this is equivalently...

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...

these problems is discussed in the paper, titled "A Poset Version of Ramanujan Results on Eulerian Numbers and Zeta Values," authored by Eric R. Dolores-Cuenca...

algebraic combinatorics, forming the simplest example of a differential poset in the sense of Stanley (1988). It is also closely connected with the crystal...

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