Normalized Matching Property of a Class of Posets Consisting of Subspaces

Normalized matching and nested chain orders

A long-standing conjecture states that posets with the normalized matching property are nested chain orders. We verify this conjecture for posets of rank 2.

Normalized Matching Property of a Class of Subspace Lattices

Let Vn(q) be the n-dimensional vector space over the finite field with q elements and K a selected k-dimensional subspace of Vn(q). Let C[n, k, t] denote the set of all subspaces S’s such that dim(S ∩K) ≥ t. We show that C[n, k, t] has the normalized matching property, which yields that C[n, k, t] has the strong Sperner property and the LYM property.

A Finite Word Poset

Our word posets have finite words of bounded length as their elements, with the words composed from a finite alphabet. Their partial ordering follows from the inclusion of a word as a subsequence of another word. The elemental combinatorial properties of such posets are established. Their automorphism groups are determined (along with similar result for the word poset studied by Burosch, Frank ...

Properties of products for flatness in the category of $S$-posets

This paper is devoted to the study of products of classes of right $S$-posets possessing one of the flatness properties and preservation of such properties under products. Specifically, we characterize a pomonoid $S$ over which its nonempty products as right $S$-posets satisfy some known flatness properties. Generalizing this results, we investigate products of right $S$-posets satisfying Condi...

A New Class of Banach Sequence Spaces