Feihu Liu

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20232026

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21 papers · 1 filter

math.CO2026

Taylor Positivity of Ehrhart Polynomials

Feihu Liu, Zihao Zhang

Let $P$ be a $d$ -dimensional lattice polytope with Ehrhart polynomial $L_{P} (t)$ . Motivated by the study of Ehrhart positivity and magic positivity, we investigate the Taylor coeffic…

math.CO2026

Hankel Transform and $(α, β)$ Somos-4 Sequences

Feihu Liu, Ying Wang, Zihao Zhang

An $(α, β)$ Somos- $4$ sequence $S_{n}$ is defined by the recurrence $S_{n} S_{n - 4} = α S_{n - 1} S_{n - 3} + β S_{n - 2}^{2}$ ( $n \geq 4$ ), with suitable initial values, where $α$ and $β$ are constant p…

math.CO2026

Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions

Feihu Liu, Jinlong Tang, Guoce Xin +1

For a finite sequence of positive integers $a = (a_{1}, \dots, a_{n})$ , the restricted partition function $q_{a} (k)$ denote the number of nonnegative integer solu…

math.CO2026

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…

math.CO2026

Magic Positivity for the Ehrhart Polynomials of Partial Permutohedra

Feihu Liu, Zihao Zhang

For positive integers $m,n$, the partial permutohedron $P (m, n)$ is a lattice polytope constructed as the convex hull of vectors in ${0, 1, \dots, n}^{m}$ that have dist…

math.CO2026

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…

Taylor Positivity of Ehrhart Polynomials

Hankel Transform and (α,β) Somos-4 Sequences

Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions

Proof of Barry's Four Hankel Determinant Conjectures

Magic Positivity for the Ehrhart Polynomials of Partial Permutohedra

Ehrhart Theory of the Join of Two Lattice Polytopes

Hankel Transform and $(α, β)$ Somos-4 Sequences