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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…
Order Polytopes of Dimension are Ehrhart Positive
Feihu Liu, Guoce Xin, Zihao Zhang
The order polytopes arising from the finite poset were first introduced and studied by Stanley. For any positive integer , Liu and Tsuchiya proved that there exists a non…
On -partitions Extended by Two-Rowed Plane Partitions
Jingxuan Li, Feihu Liu, Guoce Xin
Inspired by Gansner's elegant -trace generating function for rectangular plane partitions, we introduce two novel operators, and , along with their combinatorial…
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…
A Fast Algorithm for Denumerants with Three Variables
Feihu Liu, Guoce Xin
Let be distinct positive integers such that and . For any non-negative integer , the denumerant function denotes the number of soluti…
Three Simple Reduction Formulas for the Denumerant Functions
Feihu Liu, Guoce Xin, Chen Zhang
Let be a nonempty set of positive integers. The restricted partition function denotes the number of partitions of with parts in . When the elements in are p…
Simple Generating Functions for Certain Young Tableaux with Periodic Walls
Feihu Liu, Guoce Xin
Recently, Banderier et. al. considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. We count the…