8 citations · 26 across the 28 of their papers we have counts for
13 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…
Ehrhart Properties under Operations on Lattice Polytopes
Feihu Liu
This paper investigates the preservation of three classes of Ehrhart properties under various operations on lattice polytopes. These operations include Cartesian products, lattice…
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…
Hankel Transform and Somos-4 Sequences
Feihu Liu, Ying Wang, Zihao Zhang
An Somos- sequence is defined by the recurrence (), with suitable initial values, where and are constant p…
Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions
Feihu Liu, Jinlong Tang, Guoce Xin +1
For a finite sequence of positive integers , the restricted partition function denote the number of nonnegative integer solu…
Proof of Barry's Four Hankel Determinant Conjectures
Feihu Liu, Ying Wang, Zihao Zhang
Barry introduced a central transform of integer sequences and proposed four conjectures concerning the Hankel transforms of central transform of four rational families. We prove 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…
Ehrhart Theory of the Join of Two Lattice Polytopes
Feihu Liu, Sihao Tao, Guoce Xin
Inspired by research on the Cartesian product of two lattice polytopes, this paper investigates the Ehrhart theory of the join of two lattice polytopes. This is also a well-known o…
Unimodular Equivalence of Integral Simplices
Feihu Liu, Sihao Tao, Guoce Xin
Testing the unimodular equivalence of two full-dimensional integral simplices can be reduced to testing unimodular permutation (UP) equivalence of two nonsingular matrices. We cond…
Proof of a Conjecture on Young Tableaux with Walls
Zhicong Lin, Feihu Liu, Jiahang Liu +2
Banderier, Marchal, and Wallner considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. In this w…