10 papers · 1 filter
Ehrhart positivity for paving positroids
Feihu Liu, Zihao Zhang
A central conjecture of Ferroni, Jochemko, and Schröter posits that every positroid is Ehrhart positive. While Ehrhart positivity has recently been verified for notable classes suc…
Two families of Hermite normal form simplices
Feihu Liu, Jinlong Tang, Sihao Tao +1
We study Ehrhart coefficients, the integer decomposition property, and unimodular triangulations for two families of Hermite normal form simplices considered by Bruckamp, Caicedo,…
Counterexamples to the Mu--Welker recursive decomposition in every degree
Feihu Liu, Ying Wang, Zihao Zhang
The well-known open problem of Bell and Skandera asks whether a real-rooted polynomial with positive integer coefficients and constant term one is the -polynomial of a si…
Unimodality for IDP Lattice Simplices of Prime Normalized Volume
Feihu Liu, Zihao Zhang
Recently, Ferroni constructed a family of counterexamples to the well-known conjecture in Ehrhart theory stating that the -polynomial of a lattice polytope with the integer de…
Taylor Positivity of Ehrhart Polynomials
Feihu Liu, Zihao Zhang
Let be a -dimensional lattice polytope with Ehrhart polynomial . Motivated by the study of Ehrhart positivity and magic positivity, we investigate the Taylor coeffic…
The Ehrhart series of magic squares of orders seven and eight
Dun Qiu, Guoce Xin, Zihao Zhang
Let count the nonnegative integer matrices whose row sums, column sums, main-diagonal sum, and antidiagonal sum are all . We determine the Ehrhar…
A polynomial time algorithm for almost bounded denumerant
Guoce Xin, Chen Zhang, Zihao Zhang
Sylvester's denumerant counts the number of nonnegative integer solutions to , where is a se…
Polynomial-Time Lattice-Point Counting without Barvinok Decomposition
Guoce Xin, Zihao Zhang
By using constant term manipulations, we present the first polynomial-time algorithm for lattice-point counting in fixed dimension that does not rely on Barvinok's unimodular decom…
Polynomial-Time Evaluation of Aardal-Lenstra Denumerants via Constant Term Method
Jinlong Tang, Guoce Xin, Zihao Zhang
Aardal and Lenstra systematically studied hard knapsack problems of the form , where , is a coprime pair of positive integers, and th…
Magic Positivity for the Ehrhart Polynomials of Partial Permutohedra
Feihu Liu, Zihao Zhang
For positive integers \(m,n\), the partial permutohedron is a lattice polytope constructed as the convex hull of vectors in that have dist…