On a conjecture about the µ-permanent

Author: da Fonseca, C. M.

Source: Linear and Multilinear Algebra, Volume 53, Number 3, June 2005 , pp. 225-230(6)

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Abstract:

Let A =( a ij ) be an n -by- n matrix. For any real µ, define the polynomial where l (s) is the number of inversions of the permutation s in the symmetric group Sn . We prove that P µ (A) is a strictly increasing function of µ ? [-1,1], for a Hermitian positive definite nondiagonal matrix A , whose graph is a tree.

Keywords: Hermitian matrix; Permanent; Determinant; Digraph; Tree; 15A45; Mathematics Subject Classifications: 15A15; 05C50; 05C20

Document Type: Research article

DOI: http://dx.doi.org/10.1080/03081080500092372

Affiliations: 1: Communicated by R.B. Bapat

Publication date: 2005-06-01