MINIMUM PERMANENTS OF DOUBLY STOCHASTIC MATRICES WITH k DIAGONAL p×p BLOCK SUBMATRICES

Abstract

For positive integers $\kappa$ and p$\geq$3, let(equation omitted) where $J_{p}$ is the p${\times}$p matrix whose entries are all 1. Then, we determine the minimum permanents and minimizing matrices over (1) the face of $\Omega$(D) and (2) the face of $\Omega$($D^{*}$), where (equation omitted).

Keywords

permanent;doubly stochastic matrix;barycentric matrix

File

Download PDF

References

1. Linear Algrbra Appl. v.108 Minimum permanents on certain faces of matrices containing an identity submatrix S.Z.Song https://doi.org/10.1016/0024-3795(88)90192-9
2. Linear and Multilinear Algebra v.17 no.1 An interesting face of the polytope of doubly stochastic matrices R.A.Bruadi https://doi.org/10.1080/03081088508817637
3. Linear and Multilinear Algebra v.30 no.1-2 Some rationally looking faces of $\Omega_n$ having irrational minimum permanents Seok-Su Do;S.G.Hwang https://doi.org/10.1080/03081089108818097
4. Linear Algebra Appl. v.32 On the minimum value of rhe permanent of a nearly decomposable doubly stochastic matrix T.H.Foregger https://doi.org/10.1016/0024-3795(80)90008-7
5. J. Combinatorial Theory Ser. A. v.22 no.2 Convex polyhedra of doubly stochastic matrices Ⅰ: Application of the permanent function R.A.Brualidi;P.M.Gibson https://doi.org/10.1016/0097-3165(77)90051-6

Cited by

1. Remarks and open problems on the minimum permanent of acyclic doubly stochastic matrices vol.61, pp.3, 2013, https://doi.org/10.1080/03081087.2012.675332