5 citations · 9 across the 3 of their papers we have counts for
8 papers · 1 filter
Subdivisions of Shellable Complexes
Max Hlavacek, Liam Solus
In geometric, algebraic, and topological combinatorics, the unimodality of combinatorial generating polynomials is frequently studied. Unimodality follows when the polynomial is (r…
Some Algebraic Properties of Lecture Hall Polytopes
Petter Brändén, Liam Solus
In this note, we investigate some of the fundamental algebraic and geometric properties of -lecture hall simplices and their generalizations. We show that all -lecture hall o…
Symmetric decompositions and real-rootedness
Petter Brändén, Liam Solus
In algebraic, topological, and geometric combinatorics inequalities among the coefficients of combinatorial polynomials are frequently studied. Recently a notion called the alterna…
Local -Polynomials of Some Weighted Projective Spaces
Liam Solus
There is currently a growing interest in understanding which lattice simplices have unimodal local -polynomials (sometimes called box polynomials); specifically in light of…
Derangements, Ehrhart Theory, and Local h-polynomials
Nils Gustafsson, Liam Solus
The Eulerian polynomials and derangement polynomials are two well-studied generating functions that frequently arise in combinatorics, algebra, and geometry. When one makes an appe…
On the Relationship Between Ehrhart Unimodality and Ehrhart Positivity
Fu Liu, Liam Solus
For a given lattice polytope, two fundamental problems within the field of Ehrhart theory are to (1) determine if its (Ehrhart) -polynomial is unimodal and (2) to determine…