42 citations · 42 across the 9 of their papers we have counts for
4 papers · 1 filter
On Ward Numbers and Increasing Schröder Trees
Elena L. Wang, Guoce Xin
The Ward numbers combinatorially enumerate set partitions with block sizes and phylogenetic trees (total partition trees). We prove that also counts \emp…
Closed-Form Decomposition for Simplicial Cones and PDBarv Algorithm for Lattice Point Counting
Sihao Tao, Guoce Xin, Zihao Zhang
Counting lattice points within a rational polytope is a foundational problem with applications across mathematics and computer science. A key approach is Barvinok's algorithm, whic…
Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle
Jinlong Tang, Guoce Xin
This paper resolves an open problem raised by Ekhad and Zeilberger for computing , which is related to Stern's triangle. While , defined as the sum of squared coeff…
A combinatorial simplicial cone decomposition
Guoce Xin, Xinyu Xu, Zihao Zhang
This paper introduces an algebraic combinatorial approach to simplicial cone decompositions, a key step in solving inhomogeneous linear Diophantine systems and counting lattice poi…