Work

Sharp volume and multiplicity bounds for Fano simplices

Year: 2024

Type: article

Abstract: We present sharp upper bounds on the volume, Mahler volume and multiplicity for Fano simplices depending on the dimension and Gorenstein index. These bounds rely on the interplay between lattice simplices and unit fraction partitions. Moreover, we present an efficient procedure for explicitly classifying Fano simplices of any dimension and Gorenstein index, and we carry out the classification up to dimension four for various Gorenstein indices.

Source: Journal of Algebraic Combinatorics

DOI: 10.1007/s10801-024-01366-3

Author: Andreas Bäuerle

Institution: University of Tübingen

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Eberhard Karls Universität Tübingen