Geodesic
A conjecture on minimum permanents
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 1, pp. 273-282

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We consider the permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square $(0,1)$-matrices containing the identity submatrix. We show that a conjecture in K. Pula, S. Z. Song, I. M. Wanless (2011), is true for some cases by determining the minimum permanent on some faces of the polytope of doubly stochastic matrices.
We consider the permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square $(0,1)$-matrices containing the identity submatrix. We show that a conjecture in K. Pula, S. Z. Song, I. M. Wanless (2011), is true for some cases by determining the minimum permanent on some faces of the polytope of doubly stochastic matrices.
DOI : 10.21136/CMJ.2023.0186-23
Classification : 15A15
Keywords: permanent; doubly stochastic; barycentric; cohesive matrix 
Cheon, Gi-Sang; Song, Seok-Zun. A conjecture on minimum permanents. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 1, pp. 273-282. doi: 10.21136/CMJ.2023.0186-23
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