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A conjecture on minimum permanents

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Abstract

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.

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References

  1. R. A. Brualdi: An interesting face of the polytope of doubly stochastic matrices. Linear Multilinear Algebra 17 (1985), 5–18.

    Article  MathSciNet  Google Scholar 

  2. T. H. Foregger: On the minimum value of the permanent of a nearly decomposable doubly stochastic matrix. Linear Algebra Appl. 32 (1980), 75–85.

    Article  MathSciNet  Google Scholar 

  3. K. Pula, S.-Z. Song, I. M. Wanless: Minimum permanents on two faces of the polytope of doubly stochastic matrices. Linear Algebra Appl. 434 (2011), 232–238.

    Article  MathSciNet  Google Scholar 

  4. S.-Z. Song: Minimum permanents on certain doubly stochastic matrices. Linear Algebra Appl. 143 (1991), 49–56.

    Article  MathSciNet  Google Scholar 

  5. S.-Z. Song, L. B. Beasley: A face of the polytope of doubly stochastic matrices. To appear in Linear Multilinear Algebra.

  6. S.-Z. Song, S. M. Hong, Y.-B. Jun, S.-J. Kim: Minimum permanents on a face of the polytope of doubly stochastic matrices. Linear Algebra Appl. 259 (1997), 169–182.

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank the referee for valuable comments and helpful suggestions.

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Authors and Affiliations

  1. Sungkyunkwan University, Seobu-ro, Jangan-gu, Suwon, 16419, Republic of Korea

    Gi-Sang Cheon

  2. Jeju National University, 102 Jejudaehak-ro, Jeju, 63243, Republic of Korea

    Seok-Zun Song

Authors
  1. Gi-Sang Cheon
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  2. Seok-Zun Song
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Corresponding author

Correspondence to Seok-Zun Song.

Additional information

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2016R1D1A1B02006812). The first author (Gi-Sang Cheon) was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (2016R1A5A1008055).

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Cheon, GS., Song, SZ. A conjecture on minimum permanents. Czech Math J 74, 273–282 (2024). https://doi.org/10.21136/CMJ.2023.0186-23

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  • DOI: https://doi.org/10.21136/CMJ.2023.0186-23

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