4 papers
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…
Algebraic Volume for Polytope Arise from Ehrhart Theory
Guoce Xin, Xinyu Xu, Yingrui Zhang +1
Volume computation for -polytopes is fundamental in mathematics. There are known volume computation algorithms, mostly based on triangulation or signed-decompositi…
A polynomial time algorithm for calculating Fourier-Dedekind sums
Guoce Xin, Xinyu Xu
We solve an open problem proposed in the book ``Computing the continuous discretely" written by Matthias Beck and Sinai Robins. That is, we proposed a polynomial time algorithm for…
On Magic Distinct Labellings of Simple Graphs
Guoce Xin, Xinyu Xu, Chen Zhang +1
A magic labelling of a graph with magic sum is a labelling of the edges of by nonnegative integers such that for each vertex , the sum of labels of all edges in…