<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Let <italic>L</italic> be a not necessarily saturated lattice in ℤ<italic><sup>n </sup></italic>with a defining matrix <italic>B</italic>. We explicitly compute the set of circuits of <italic>L</italic> in terms of maximal minors of <italic>B</italic>. This has a variety of applications from toric to tropical geometry, from Gröbner to Graver bases, and from linear to binomial ideals.</p>
</abstract>

Let L be a not necessarily saturated lattice in ℤn with 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.

A determinantal formula for circuits of integer lattices

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"A determinantal formula for circuits of integer lattices"}

Let L be a not necessarily saturated lattice in ℤn with a defining matrix B. We explicitly compute the set of circuits of L in terms of maximal minors of B....

A determinantal formula for circuits of integer lattices

Published Online: Jan 21, 2022

Page range: 121 - 127

Received: Oct 21, 2021

Accepted: Dec 29, 2021

DOI: https://doi.org/10.2478/aupcsm-2021-0008

Keywords
Non-saturated lattices, circuits

© 2021 Hossein Sabzrou, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

A determinantal formula for circuits of integer lattices

Published Online: Jan 21, 2022

Page range: 121 - 127

Received: Oct 21, 2021

Accepted: Dec 29, 2021

DOI: https://doi.org/10.2478/aupcsm-2021-0008

KeywordsNon-saturated lattices, circuits

© 2021 Hossein Sabzrou, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
Non-saturated lattices, circuits