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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…
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…
The Frobenius problem for a class of quotients of numerical semigroups
Feihu Liu
Given a numerical semigroup and a positive integer , the quotient also forms a numerical semigroup. In this paper, we first ch…
Generating functions for the quotients of numerical semigroups
Feihu Liu
We propose a class of generating functions denoted by , which is related to the Sylvester denumerant for the quotients of numerical semigroups. Using MacMahon's…