6 papers · 1 filter
Relaxed coparking functions and Stanley's conjecture for matroid -vectors
SuHo Oh
Stanley's conjecture asserts that the -vector of a matroid is a pure -sequence. Corry, Dochtermann, McClain, Perkinson and Yi introduced cycle systems, which give a bijective…
Parking functions and chip-firing on hypergraphs
Timothy Blanton, Anton Dochtermann, Isabelle Hong +2
For a connected graph with sink vertex , a -parking function is a vector of nonnegative integers whose entries are determined by cut-sets in . Such objects also arise…
Extendability of -decomposable complexes
Rhea Ghosal, Melody Han, Benjamin Keller +5
A well-known conjecture of Simon (1994) states that any pure -dimensional shellable complex on vertices can be extended to , the -skeleton of the -d…
Permutation ensembles on products of simplices
SuHo Oh
We propose the study of -ensembles: arrays of permutations of that encode the boundary data of . We develop a general toolkit for these ensembles,…
On z-Superstable and Critical Configurations of Chip Firing Pairs
Zach Benton, Jane Kwak, SuHo Oh +2
It is well known that there is a duality map between the superstable configurations and the critical configurations of a graph. This was extended to all M-matrices in (Guzmàn-Kliva…
Gap between the number of facets of the two poset polytopes
Binaya Bhandari, Debra Cunningham, Grace Morrell +2
We study the difference between the number of facets of the order polytope and the chain polytope of a poset. Hibi and Li classified posets where the gap is exactly zero. We descri…