1 citations · 2 across the 7 of their papers we have counts for
12 papers
Ehrhart Limits
Benjamin Braun, McCabe Olsen
We introduce the definition of an Ehrhart limit, that is, a formal power series with integer coefficients that is the limit in the ring of formal power series of a sequence of Ehrh…
Lattice polytopes from Schur and symmetric Grothendieck polynomials
Margaret Bayer, Bennet Goeckner, Su Ji Hong +5
Given a family of lattice polytopes, two common questions in Ehrhart Theory are determining when a polytope has the integer decomposition property and determining when a polytope i…
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…
Level algebras and -lecture hall polytopes
Florian Kohl, McCabe Olsen
Given a family of lattice polytopes, a common endeavor in Ehrhart theory is the classification of those polytopes in the family that are Gorenstein, or more generally level. In thi…
Hilbert Bases and Lecture Hall Partitions
McCabe Olsen
In the interest of finding the minimum additive generating set for the set of -lecture hall partitions, we compute the Hilbert bases for the -lectur…
Flag Descents and Eulerian Polynomials for Wreath Product Quotients
Dustin Hedmark, Cyrus Hettle, McCabe Olsen
We investigate the -colored Eulerian polynomials and a notion of descents introduced in a recent paper of Hedmark and show that such polynomials can be computed as a polynomial…
Gorenstein properties and integer decomposition properties of lecture hall polytopes
Takayuki Hibi, McCabe Olsen, Akiyoshi Tsuchiya
Though much is known about -lecture hall polytopes, there are still many unanswered questions. In this paper, we show that -lecture hall polytopes satisfy the int…
Self dual reflexive simplices with Eulerian polynomials
Takayuki Hibi, McCabe Olsen, Akiyoshi Tsuchiya
A lattice polytope is called reflexive if its dual is a lattice polytope. The property that is unimodularly equivalent to $\mathcal{P…
Euler-Mahonian statistics and descent bases for semigroup algebras
Benjamin Braun, McCabe Olsen
We consider quotients of the unit cube semigroup algebra by particular -invariant ideals. Using Gröbner basis methods, we show that the resulting graded quotie…