7 papers · 1 filter
A polynomial time algorithm for almost bounded denumerant
Guoce Xin, Chen Zhang, Zihao Zhang
Sylvester's denumerant counts the number of nonnegative integer solutions to , where is a se…
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…
A proof of Xin-Zhang's tridiagonal determinant conjecture (extended version)
Jiaqiang Hu, Chen Zhang
We confirm a recent conjecture of Xin and Zhang, which establishes a simple product formula for the characteristic polynomial of an tridiagonal matrix . Thi…
Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS
Feihu Liu, Guoce Xin, Chen Zhang
In this paper, we provide an overview of Ehrhart polynomials associated with order polytopes of finite posets, a concept first introduced by Stanley. We focus on their combinatoria…
A variation of the Morris constant term
Guoce Xin, Chen Zhang
The Morris constant term identity is important due to its equivalence with the well-known Selberg integral. We find a variation of the Morris constant term, denoted , in th…
A polynomial time algorithm for Sylvester waves when entries are bounded
Guoce Xin, Chen Zhang
The Sylvester's denumerant \( d(t; \boldsymbol{a}) \) is a quantity that counts the number of nonnegative integer solutions to the equation \( \sum_{i=1}^{N} a_i x_i = t \), where…