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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...
The poset of the nilpotent commutator of a nilpotent matrix
Jordan type nilpotent matrix commutator poset
2012/2/29
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...
Discrete Morse theory and the consecutive pattern poset
consecutive pattern discrete Morse theory factor order Mobius function permutation patters posets
2011/9/13
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...
The secretary problem on an unknown poset
classical secretary problem maximal elements algorithm Combinatorics Probability
2011/8/26
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...
Poset pinball, highest forms, and (n-2,2) Springer varieties
Poset pinball highest forms (n-2,2) Springer varieties
2011/2/25
In this manuscript we study type A nilpotent Hessenberg varieties equipped with a natural S1-
action using techniques introduced by Tymoczko.
Poset pinball, the dimension pair algorithm, and type A regular nilpotent Hessenberg varieties
Poset pinball the dimension pair algorithm type regular nilpotent Hessenberg varieties
2011/2/22
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 ...
Properties of the poset of Dyck paths ordered by inclusion
Dyck paths ordered by inclusion math
2010/11/24
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...