Feihu Liu

activity

20232026

most citedGenerating functions for the quotients of numerical semigroups

1 citations · 1 across the 6 of their papers we have counts for

collaborators

6 papers

math.NT2026

On the Frobenius Number of Quotients of Numerical Semigroups

Feihu Liu

Given a numerical semigroup $S$ and a positive integer $p$ , the quotient $\frac{S}{p} = {n \in N ∣ p n \in S}$ also forms a numerical semigroup. When $S=\langle a,b\rangle…

math.CO2026

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 $d \geq 3$ and integers $1 \leq i_{1} < \dots < i_{k} \leq d - 2$ , does there exist a $d$ -dimensiona…

math.CO2026

Proofs of four generating function conjectures for arbor polytopes

Feihu Liu, Jinlong Tang

This paper proves four conjectured generating series, due to Chapoton, which concern invariants of posets and polytopes associated with a specific sequence of arbors. Two of these…

math.CO2026

The Frobenius problem for a class of quotients of numerical semigroups

Feihu Liu

Given a numerical semigroup $S$ and a positive integer $p$ , the quotient $\frac{S}{p} = {x \in N ∣ p x \in S}$ also forms a numerical semigroup. In this paper, we first ch…

math.CO2024★ 1 cited

Generating functions for the quotients of numerical semigroups

Feihu Liu

We propose a class of generating functions denoted by $RGF_{p} (x)$ , which is related to the Sylvester denumerant for the quotients of numerical semigroups. Using MacMahon's…

math.NT2023

On quotients of numerical semigroups for almost arithmetic progressions

Feihu Liu

Let $⟨ A ⟩$ be the numerical semigroup generated by relatively prime positive integers ${a_{1}, a_{2}, ..., a_{n}}$ . The quotient of $⟨ A ⟩$ with respect to a positi…