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A determinantal formula for circuits of integer lattices

Hossein Sabzrou

Hossein Sabzrou

School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran
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Sabzrou, Hossein
  
Jan 21, 2022
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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
© 2021 Hossein Sabzrou, published by Sciendo
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

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.

Language:
English
Publication timeframe:
1 times per year
Journal Subjects:
Mathematics, General Mathematics
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