3 papers
math.CO2022
Lattice Minors and Eulerian Posets
William Gustafson
We introduce posets of simple vertex labeled minors of graphs and a generalization to the level of polymatroids, collectively termed minor posets. We show that any minor poset is i…
math.CO2021
Polymatroids, closure operators and lattices
William Gustafson
We study the closure operators of polymatroids from a lattice theoretic point of view. We show that polymatroid closure operators relate to lattices enriched with a generating set…
math.CO2020
Counterexample to a conjecture of Ziegler concerning a simple polytope and its dual
William Gustafson
Problem 4.19 in Ziegler's "Lectures on Polytopes" asserts that every simple -dimensional polytope has the property that its dual can be constructed as the convex hull of a subse…