Multivariate volume, Ehrhart, and h⁎-polynomials of polytropes. (January 2023)

• Record Type: Journal Article
• Authors: Brandenburg, Marie-Charlotte; Elia, Sophia; Zhang, Leon
• Is Part Of: Journal of symbolic computation. Volume 114(2023)
• Page Start: 209
• Page End: 230
• Publication Date: 2023-01
• Subjects: Polytropes -- Alcoved polytopes -- Volume polynomials -- Ehrhart theory; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.04.011
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The univariate Ehrhart and h ⁎ -polynomials of lattice polytopes have been widely studied. We describe methods from toric geometry for computing multivariate versions of volume, Ehrhart and h ⁎ -polynomials of lattice polytropes, which are both tropically and classically convex, and are also known as alcoved polytopes of type A . These algorithms are applied to all polytropes of dimensions 2, 3 and 4, yielding a large class of integer polynomials. We give a complete combinatorial description of the coefficients of volume polynomials of 3-dimensional polytropes in terms of regular central subdivisions of the fundamental polytope. Finally, we provide a partial characterization of the analogous coefficients in dimension 4.