6 papers
Two families of Hermite normal form simplices
Feihu Liu, Jinlong Tang, Sihao Tao +1
We study Ehrhart coefficients, the integer decomposition property, and unimodular triangulations for two families of Hermite normal form simplices considered by Bruckamp, Caicedo,…
Ehrhart Theory of the Join of Two Lattice Polytopes
Feihu Liu, Sihao Tao, Guoce Xin
Inspired by research on the Cartesian product of two lattice polytopes, this paper investigates the Ehrhart theory of the join of two lattice polytopes. This is also a well-known o…
Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern
Feihu Liu, Sihao Tao, Guoce Xin
In Ehrhart theory, the well-known sign pattern problem asks: given a positive integer and integers , does there exist a -dimensiona…
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…
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]^…
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…