The permanent of a class of matrices associated with a finite group
In: Linear and Multilinear Algebra, Jg. 42 (1997), Heft 4, S. 323-347
Online
serialPeriodical
Zugriff:
Let g be a convex functiong[α,β]→Rg≥0. For a finite group G,G={g1,…gn}, a function π:G→[α,β], and an integer k,1≤k≤n, the following function h:[0,1]→R is considered:for0≤t≤1 let h(t) be the sum of the permanents of all kxk submatrices of the nxn nonnegative matrix[image omitted] where γ=ΣxεGπ(x). Set α0=min π(G),β0=min π(G). It is proved that h is decreasing on [0,1]. In additionh(t1)=h(t2) for given 0≤t1≤t21 if and only if on the segment[image omitted] the function g is either constant and 1≤k≤n, or linear and k=1. considering the case g(x)=x,0≤x≤1, and γ=1, we have a certain class of doubly stochastic matrices for which the Djokovic conjecture about monotonicity is true. This class includes all the doubly stochastic circulant matrices
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The permanent of a class of matrices associated with a finite group
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Autor/in / Beteiligte Person: | Falikman, Dmitry |
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Zeitschrift: | Linear and Multilinear Algebra, Jg. 42 (1997), Heft 4, S. 323-347 |
Veröffentlichung: | 1997 |
Medientyp: | serialPeriodical |
ISSN: | 0308-1087 (print) ; 1563-5139 (print) |
DOI: | 10.1080/03081089708818508 |
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