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Given square matrices B and B0 with a poset-indexed block structure (for which an ij block is zero unless i 1 j), when are there invertible matrices U and V with this required-zero-block structure suc...
In this work we prove that a poset-block space admits a MacWilliams-type identity if and only if the poset is hierarchical and at any level of the poset, all the blocks have the same dimension. When t...
Fix an n by n nilpotent matrix B with entries in an infinite field k. Assume that B is in Jordan canonical form with associated Jordan block partition P. It is well known that the nilpotent commutator...
Abstract: The class of poset metrics is very large and contains some interesting families of metrics. A family of metrics, based on posets which are formed from disjoint chains which have the same siz...
Abstract: We use discrete Morse theory to provide another proof of Bernini, Ferrari, and Steingrimson's formula for the Mobius function of the consecutive pattern poset. In addition, we are able to de...
Abstract: Felsner and Reuter introduced the linear extension diameter of a partially ordered set $\mathbf{P}$, denoted ${led}(\mathbf{P})$, as the maximum distance between two linear extensions of $\m...
Abstract: We consider generalizations of the classical secretary problem, also known as the problem of optimal choice, to posets where the only information we have is the size of the poset and the num...
In this manuscript we study type A nilpotent Hessenberg varieties equipped with a natural S1- action using techniques introduced by Tymoczko.
In thismanuscript we develop the theory of poset pinball, a combinatorial game recently introduced by Harada and Tymoczko for the study of the equivariant cohomology rings of GKM-compatible subspaces ...
An expository summary of properties of the poset of Dyck paths ordered by inclusion.
For a standard graded algebra R, we consider embeddings of the the poset of Hilbert functions of quotients of R into the poset of ideals of R, as a way of classification of Hilbert functions. There a...

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