3 papers
math.CO2026
Unimodular Equivalence of Integral Simplices
Feihu Liu, Sihao Tao, Guoce Xin
Testing the unimodular equivalence of two full-dimensional integral simplices can be reduced to testing unimodular permutation (UP) equivalence of two nonsingular matrices. We cond…
math.CO2025
The Sign Pattern Problem for Ehrhart Polynomials
Feihu Liu, Sihao Tao, Guoce Xin
We investigate the sign patterns of coefficients in the Ehrhart polynomial of the Cartesian product between the -th pyramid over the Reeve tetrahedron and the hypercube $[0, n]^…
math.CO2025
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…