Let 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1, . . . , n} ordered by inclusion. Recall that 2[n] may be partitioned into what we call the canonical symmetric chain decomposition (due to de Bruijn, Tengbergen, and Kruyswijk), or CSCD. Motivated by a question of Füredi, we show that there exists a function d(n) ∼ 1 2 √ n such that for any n ≥ 0, 2[n] may be p...

We study the poset of Borel congruence classes of symmetric matrices ordered by containment of closures. We give a combinatorial description of this poset and calculate its rank function. We discuss the relation between this poset and the Bruhat poset of involutions of the symmetric group. Also we present the poset of Borel congruence classes of anti-symmetric matrices ordered by containment of...

In this paper we study topological properties of the poset of injective words and the lattice of classical non-crossing partitions. Specifically, it is shown that after the removal of the bottom and top elements (if existent) these posets are doubly Cohen-Macaulay. This extends the well-known result that those posets are shellable. Both results rely on a new poset fiber theorem, for doubly homo...

In 2001, the notion of a fuzzy poset defined on a set X via a triplet (L,G, I) of functions with domain X ×X and range [0, 1] satisfying a special condition L+G+ I = 1 is introduced by J. Negger and Hee Sik Kim, where L is the ‘less than’ function, G is the ‘greater than’ function, and I is the ‘incomparable to’ function. Using this approach, we are able to define a special class of fuzzy poset...

A special case of the Generalized Baues Conjecture states that the order complex of the Baues poset of an acyclic vector connguration A (the Baues complex of A) is homotopy equivalent to a sphere of dimension equal to the corank of A minus one. The Baues poset of A is the set of proper polyhedral subdivisions of A ordered by reenement. Recently, Santos has found a counterexample in corank 317 t...

We show that the order complex of poset nonempty intervals, ordered by inclusion, is a Tchebyshev triangulation original poset. Besides studying properties this transformation, we dual type B permutohedron combinatorially equivalent to suspension intervals Boolean algebra (with minimum and maximum elements removed).

New q-analogs of Stirling numbers of the second kind(and the first kined) are derived from a poset on [2k] using Stanley’s P -partition theory [?]. We also generalize to the poset on the set [rk].