Open AccessA determinantal formula for circuits of integer lattices
Author(s) -
Hossein Sabzrou
Publication year - 2021
Publication title -
annales universitatis paedagogicae cracoviensis studia mathematica
Language(s) - English
Resource type - Journals
eISSN - 2300-133X
pISSN - 2081-545X
DOI - 10.2478/aupcsm-2021-0008
Subject(s) - toric variety , variety (cybernetics) , mathematics , lattice (music) , binomial (polynomial) , integer (computer science) , binomial coefficient , pure mathematics , set (abstract data type) , combinatorics , matrix (chemical analysis) , electronic circuit , discrete mathematics , algebra over a field , computer science , physics , statistics , materials science , quantum mechanics , acoustics , composite material , programming language
Let L be a not necessarily saturated lattice in ℤ n 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.