A determinantal formula for circuits of integer lattices

Hossein Sabzrou

doi:10.2478/aupcsm-2021-0008

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A determinantal formula for circuits of integer lattices

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 20 (2021): Issue 1 (January 2021)

By: Hossein Sabzrou

Open Access

|Jan 2022

Abstract

Let L be a not necessarily saturated lattice in ℤⁿwith a defining matrix B. We explicitly compute the set of circuits of L in terms of maximal minors of B. This has a variety of applications from toric to tropical geometry, from Gröbner to Graver bases, and from linear to binomial ideals.

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Articles in this issue

DOI: https://doi.org/10.2478/aupcsm-2021-0008 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 121 - 127

Submitted on: Oct 21, 2021

Accepted on: Dec 29, 2021

Published on: Jan 21, 2022

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Non-saturated lattices,

circuits

Related subjects:

Mathematics,

General mathematics

© 2022 Hossein Sabzrou, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 20 (2021): Issue 1 (January 2021)