On the Coefficients of the Permanent and the Determinant of a Circulant\n Matrix. Applications

2018/06/15 by Liena Colarte-Gómez, Emilia Mezzetti, Colarte, Liena +5
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1806.05905

openalex publication_date 2018/06/15 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Let d(N ) (resp. p(N )) be the number of summands in the determinant\n(resp. permanent) of an N\× N circulant matrix A = (a_ij ) given by\na_ij = X_i+j where i + j should be considered mod N . This short\nnote is devoted to prove that d(N ) = p(N ) if and only if N is a prime\npower. We then give an application to homogeneous monomial ideals failing the\nWeak Lefschetz property.\n

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