2018/04/06 by Carlos M. da Fonseca, da Fonseca, Carlos M.
Computer Science · Engineering · Mathematics · #05C20 #05C50 #15A15 #15A45 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #graph theory and CDMA systems #math.CO #msc:05C20 #msc:05C50 #msc:15A15 #msc:15A45
paper · pdf · doi:10.48550/arxiv.1804.02231
This manuscript is largely based on the talk "On a generalization of the determinant of a matrix" that the author gave in Washington \& Lee University, Lexington, VA, USA, on July 19, 2012. It was submitted to Linear and Multilinear Algebra on September 20, 2015. A reduced form will be published as a Letter to the Editor in the same journal
arxiv created 2018/04/06 · openalex publication_date 2018/04/06 · arxiv updated 2018/04/09 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
Let A=(aij) be an n-by-n matrix. For any real number μ, we define the polynomial Pμ(A)=∑σ∈ Sn a1σ(1)⋯ anσ(n) μℓ(σ) , as the μ-permanent of A, where ℓ(σ) is the number of inversions of the permutation σ in the symmetric group Sn. In this note, we review several less known results of the μ-permanent, recalling some of its interesting properties. Some determinantal conjectures are considered and extended to that polynomial. A correction to a previous note is presented as well.