Journal of Combinatorics

Volume 11 (2020)

Number 3

Classification of lattice polytopes with small volumes

Pages: 495 – 509

DOI: https://dx.doi.org/10.4310/JOC.2020.v11.n3.a4

Authors

Takayuki Hibi (Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka, Japan)

Akiyoshi Tsuchiya (Graduate school of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo, Japan)

Abstract

In the frame of a classification of general square systems of polynomial equations solvable by radicals, Esterov and Gusev succeeded in classifying all spanning lattice polytopes whose normalized volumes are at most $4$. In the present paper, we complete to classify all lattice polytopes whose normalized volumes are at most $4$ based on the known classification of their $\delta$-polynomials.

Keywords

lattice polytope, $\delta$-polynomial, $\delta$-vector, Ehrhart polynomial, unimodular equivalence

2010 Mathematics Subject Classification

52B12, 52B20

Full Text (PDF format)

The first-named author is partially supported by JSPS KAKENHI 19H00637.

The second-named author is partially supported by Grant-in-Aid for JSPS Fellows 16J01549.

Received 4 February 2019

Published 11 May 2020