3 papers
math.CO2025
Fast Evaluation of Generalized Todd Polynomials: Applications to MacMahon's Partition Analysis and Integer Programming
Guoce Xin, Yingrui Zhang, ZiHao Zhang
The Todd polynomials, denoted as , are characterised by their generating functions: …
math.CO2024
Inverting the General Order Sweep Map
Ying Wang, Guoce Xin, Yingrui Zhang
Building upon the foundational work of Thomas and Williams on the modular sweep map, Garsia and Xin have developed a straightforward algorithm for the inversion of the sweep map on…
math.CO2024
A Combinatorial Decomposition of Knapsack Cones
Guoce Xin, Yingrui Zhang, Zihao Zhang
In this paper, we focus on knapsack cones, a specific type of simplicial cones that arise naturally in the context of the knapsack problem . We pr…