Article
| Title: | A conjecture on minimum permanents (English) |
| Author: | Cheon, Gi-Sang |
| Author: | Song, Seok-Zun |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 273-282 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | permanent |
| Keyword: | doubly stochastic |
| Keyword: | barycentric |
| Keyword: | cohesive matrix |
| MSC: | 15A15 |
| DOI: | 10.21136/CMJ.2023.0186-23 |
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| Date available: | 2024-03-13T10:09:48Z |
| Last updated: | 2024-03-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152279 |
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| Reference: | [1] Brualdi, R. A.: An interesting face of the polytope of doubly stochastic matrices.Linear Multilinear Algebra 17 (1985), 5-18. Zbl 0564.15010, MR 0859664, 10.1080/03081088508817637 |
| Reference: | [2] Foregger, T. H.: On the minimum value of the permanent of a nearly decomposable doubly stochastic matrix.Linear Algebra Appl. 32 (1980), 75-85. Zbl 0441.15005, MR 0577907, 10.1016/0024-3795(80)90008-7 |
| Reference: | [3] Pula, K., Song, S.-Z., Wanless, I. M.: Minimum permanents on two faces of the polytope of doubly stochastic matrices.Linear Algebra Appl. 434 (2011), 232-238. Zbl 1209.15013, MR 2737245, 10.1016/j.laa.2010.08.015 |
| Reference: | [4] Song, S.-Z.: Minimum permanents on certain doubly stochastic matrices.Linear Algebra Appl. 143 (1991), 49-56. Zbl 0712.15018, MR 1077723, 10.1016/0024-3795(91)90005-H |
| Reference: | [5] Song, S.-Z., Beasley, L. B.: A face of the polytope of doubly stochastic matrices.(to appear) in Linear Multilinear Algebra. 10.1080/03081087.2023.2190073 |
| Reference: | [6] Song, S.-Z., Hong, S. M., Jun, Y.-B., Kim, S.-J.: Minimum permanents on a face of the polytope of doubly stochastic matrices.Linear Algebra Appl. 259 (1997), 169-182. Zbl 0955.15009, MR 1450536, 10.1016/s0024-3795(96)00248-0 |
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