On the coefficients of the permanent and the determinant of a circulant matrix: Applications
Copyright policy )On the coefficients of the permanent and the determinant of a circulant matrix: Applications
Let $d(N )$ (resp. $p(N )$) be the number of summands in the determinant (resp. permanent) of an $N\times N$ circulant matrix $A = (a_{ij} )$ given by $a_{ij} = X_{i+j}$ where $i + j$ should be considered $\mod N$ . This short note is devoted to prove that $d(N ) = p(N )$ if and only if $N$ is a prime power. We then give an application to homogeneous monomial ideals failing the Weak Lefschetz property.
Proc. AMS, to appear
- University of Trieste Italy
- University of Barcelona Spain
circulant matrix, monomial ideals, monomial ideal, Toeplitz, Cauchy, and related matrices, Circulant matrix; permanent,;weak Lefschetz property; Laplace equations; monomial ideals; toric varieties, weak Lefschetz property, Circulant matrix, permanent,, Laplace equation, Determinants, permanents, traces, other special matrix functions, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), permanent, Mathematics - Algebraic Geometry, FOS: Mathematics, Mathematics - Combinatorics, Commutative Artinian rings and modules, finite-dimensional algebras, Laplace equations, Matemàtiques, Combinatorics (math.CO), 51 - Matemàtiques, Algebraic Geometry (math.AG), toric varieties
circulant matrix, monomial ideals, monomial ideal, Toeplitz, Cauchy, and related matrices, Circulant matrix; permanent,;weak Lefschetz property; Laplace equations; monomial ideals; toric varieties, weak Lefschetz property, Circulant matrix, permanent,, Laplace equation, Determinants, permanents, traces, other special matrix functions, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), permanent, Mathematics - Algebraic Geometry, FOS: Mathematics, Mathematics - Combinatorics, Commutative Artinian rings and modules, finite-dimensional algebras, Laplace equations, Matemàtiques, Combinatorics (math.CO), 51 - Matemàtiques, Algebraic Geometry (math.AG), toric varieties
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