Arithmetical structures on dominated polynomials

Arithmetical structures on matrices were introduced in Corrales H, Valencia CE (Arithmetical structures on graphs. Linear Algebra Appl, 536:120–151, 2018), which are finite whenever the matrix is irreducible. We generalize the algorithm that computes arithmetical structures on matrices given in Vale...

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Bibliographic Details
Published in:São Paulo Journal of Mathematical Sciences 2023-06, Vol.17 (1), p.430-439
Main Authors: Valencia, Carlos E., Villagrán, Ralihe R.
Format: Article
Language:English
Subjects:
Algorithms
Integers
Linear algebra
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Polynomials
Special Issue in Honor of Rafael H. Villarreal on the Occasion of His 70th Birthday
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Summary:Arithmetical structures on matrices were introduced in Corrales H, Valencia CE (Arithmetical structures on graphs. Linear Algebra Appl, 536:120–151, 2018), which are finite whenever the matrix is irreducible. We generalize the algorithm that computes arithmetical structures on matrices given in Valencia CE, Villagrán RR (Algorithmic aspects of arithmetical structures. Linear Algeb Appl, 640:191–208, 2022), to an algorithm that computes arithmetical structures on dominated polynomials. A dominated polynomial is an integer multivariate polynomial, such that it contains a monomial, which is divided by all of its monomials. We give an example of a dominated polynomial which is not the determinant of an integer matrix and show how the algorithm works on it.
ISSN:1982-6907
2316-9028
2306-9028
DOI:10.1007/s40863-022-00336-6