4 papers · 1 filter
Multivariate polynomials for generalized permutohedra
Eric Katz, McCabe Olsen
Using the notion of Mahonian statistic on acyclic posets, we introduce a -analogue of the -polynomial of a simple generalized permutohedron. We focus primarily on the case of…
Unconditional reflexive polytopes
Florian Kohl, McCabe Olsen, Raman Sanyal
A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. In this paper, we investigate unconditional lattice polytopes with resp…
Birkhoff polytopes of different type and the orthant-lattice property
Florian Kohl, McCabe Olsen
The Birkhoff polytope, defined to be the convex hull of permutation matrices, is a well studied polytope in the context of the Ehrhart theory. This polytope is known to…
Polyhedral geometry for lecture hall partitions
McCabe Olsen
Lecture hall partitions are a fundamental combinatorial structure which have been studied extensively over the past two decades. These objects have produced new results, as well as…