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On the Divisibility of Permanents for (±1)-Matrices

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The classical results by Kräuter and Seifter concerning the divisibility of permanents for (±1)-matrices by large powers of 2 are useful in testing whether the permanent function is nonvanishing. This paper suggests a new approach to this problem, allowing one to obtain a short combinatorial proof of the results by Kräuter and Seifter.

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References

  1. R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Cambridge Univ. Press (1991).

  2. D. K. Faddeev and I. S. Sominskiĭ, Problems in Higher Algebra [in Russian], Nauka, Moscow (1968).

  3. A. R. Kräuter, “Recent results on permanents of (1, −1)-matrices,” Ber. Math.-Statist. Sekt. Forschungsgesellschaft Joanneum Graz, 249, 1–25 (1985).

    MATH  Google Scholar 

  4. A. R. Kräuter and N. Seifter, “On some questions concerning permanents of (1, −1)-matrices,” Isr. J. Math., 45, No. 1, 53–62 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Marcus and M. Newman, “Inequalities for the permanent function,’ Ann. Math., 75, No. 1, 47–62 (1962).

  6. H. Perfect, “Positive diagonals of ±1-matrices,” Monatsh. Math., 77, 225–240 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Reich, “Another solution of an old problem of Pólya,” Amer. Math. Monthly, 78, 649–650 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Simion and F. W. Schmidt, “On (+1, −1)-matrices with vanishing permanent,” Discrete Math., 46, 107–108 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  9. E. T. H. Wang, “On permanents of (1, −1)-matrices,” Isr. J. Math., 18, 353–361 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  10. I. M. Wanless, “Permanents of matrices of signed ones,” Linear Multilinear Algebra, 53, No. 6, 427–433 (2005).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Lomosov Moscow State University, Moscow, Russia

    M. V. Budrevich, A. E. Guterman & K. A. Taranin

Authors
  1. M. V. Budrevich
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  2. A. E. Guterman
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  3. K. A. Taranin
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Corresponding author

Correspondence to A. E. Guterman.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 439, 2015, pp. 26–37.

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Budrevich, M.V., Guterman, A.E. & Taranin, K.A. On the Divisibility of Permanents for (±1)-Matrices. J Math Sci 216, 738–745 (2016). https://doi.org/10.1007/s10958-016-2937-4

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  • DOI: https://doi.org/10.1007/s10958-016-2937-4

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