Geodesic
A conjecture on minimum permanents
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 1, pp. 273-282
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 
@article{10_21136_CMJ_2023_0186_23,
     author = {Cheon, Gi-Sang and Song, Seok-Zun},
     title = {A conjecture on minimum permanents},
     journal = {Czechoslovak Mathematical Journal},
     pages = {273--282},
     year = {2024},
     volume = {74},
     number = {1},
     doi = {10.21136/CMJ.2023.0186-23},
     mrnumber = {4717833},
     zbl = {07893378},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0186-23/}
}
TY  - JOUR
AU  - Cheon, Gi-Sang
AU  - Song, Seok-Zun
TI  - A conjecture on minimum permanents
JO  - Czechoslovak Mathematical Journal
PY  - 2024
SP  - 273
EP  - 282
VL  - 74
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0186-23/
DO  - 10.21136/CMJ.2023.0186-23
LA  - en
ID  - 10_21136_CMJ_2023_0186_23
ER  - 
%0 Journal Article
%A Cheon, Gi-Sang
%A Song, Seok-Zun
%T A conjecture on minimum permanents
%J Czechoslovak Mathematical Journal
%D 2024
%P 273-282
%V 74
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0186-23/
%R 10.21136/CMJ.2023.0186-23
%G en
%F 10_21136_CMJ_2023_0186_23
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

[1] Brualdi, R. A.: An interesting face of the polytope of doubly stochastic matrices. Linear Multilinear Algebra 17 (1985), 5-18. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[4] Song, S.-Z.: Minimum permanents on certain doubly stochastic matrices. Linear Algebra Appl. 143 (1991), 49-56. | DOI | MR | JFM

[5] Song, S.-Z., Beasley, L. B.: A face of the polytope of doubly stochastic matrices. (to appear) in Linear Multilinear Algebra. | DOI

[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. | DOI | MR | JFM

Cité par Sources :