A determinantal formula for circuits of integer lattices | Zendy

Hossein Sabzrou | Zendy

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A 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.

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