Spectrum of permanent's values and its extremal magnitudes in $Λ_n^3$ and $Λ_n(α,β,γ)$

Details Spectrum of permanent's values and its extremal magnitudes in $Λ_n^3$ and $Λ_n(α,β,γ)$ Spectrum of permanent's values and its extremal magnitudes in $Λ_n^3$ and $Λ_n(α,β,γ)$

2011-04-20

arxiv.org/abs/1104.4051v3

Mathematics

Combinatorics

22 pages

Scientific paper

Let $\Lambda_n^k$ denote the class of $(0,1)$ square matrices containing in each row and in each column exactly $k$ 1's. The minimal value of $k,$ for which the behavior of the permanent in $\Lambda_n^k$ is not quite studied, is $k=3.$ We give a simple algorithm for calculation upper magnitudes of permanent in $\Lambda_n^3$ and consider some extremal problems in a generalized class $\Lambda_n(\alpha,\beta,\gamma),$ the matrices of which contain in each row and in each column nonzero elements $\alpha,\beta,\gamma$ and $n-3$ zeros.

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