14 papers
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…
Root-of-unity weighted trigonometric power sums: a constant term approach
Jiahang Liu, Guoce Xin
We present a unified method for evaluating finite sums of powers of cotangent, tangent, cosecant and secant weighted by primitive th roots of unity. The approach relies on const…
An Algorithm for Computing Hankel Determinants up to Order
Feihu Liu, Guoce Xin, Zihao Zhang
Given the rational power series , the Hankel determinant of order is defined as $H_n(h(x)) := \det (h_{i+j})_{1 \leq i,j \le…
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…
Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern
Feihu Liu, Sihao Tao, Guoce Xin
In Ehrhart theory, the well-known sign pattern problem asks: given a positive integer and integers , does there exist a -dimensiona…
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…