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Arithmetic Matrix Operations that Preserve Conversion

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The behavior of the conversion property under arithmetic matrix operations is investigated. Bibliography: 15 titles.

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References

  1. R. A. Brualdi and B. L. Shader, “On sing-nonsigular matrices and the conversion of the permanent into the determinant,” DIMACS Ser. Discrete Math. Theor. Comput. Sci., 4, 117–134 (1991).

    MathSciNet  Google Scholar 

  2. M. V. Budrevich and A. E. Guterman, “Permanent has less zeros than determinant over finite fields,” Amer. Math. Soc., Contemp. Math., 579, 33–42 (2012).

    Article  MathSciNet  Google Scholar 

  3. M. P. Coelho and M. A. Duffner, “Immanant preserving and immanant converting maps,” Linear Algebra Appl., 418, No. 1, 177–187 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Guterman, G. Dolinar, and B. Kuz’ma, “P’olya convertibility problem for symmetric matrices,” Matem. Zametki, 92, No. 5, 624–635 (2012).

    MATH  Google Scholar 

  5. G. Dolinar, A. E. Guterman, and B. Kuz’ma, “On the Gibson barriers for the P’olya problem,” Fundam. Prikl. Matem., 16, No. 8, 73–86 (2010).

    Google Scholar 

  6. J. von zur Gathen, “Permanent and determinant,” Linear Algebra Appl., 96, 87–100 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  7. P. M. Gibson, “Conversion of the permanent into the determinant,” Proc. Amer. Math. Soc., 27, 471–476 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  8. B. Kuz’ma, “A note on immanant preservers,” Fundam. Prikl. Matem., 13, No. 4, 113–120 (2007).

    Google Scholar 

  9. C. H. C. Little, “A characterization of convertible (0;1)-matrices,” J. Combin. Theory, Ser. B, 18, 187–208 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Marcus and H. Minc, “On the relation between the determinant and the permanent,” Illinois J. Math., 5, 376–381 (1961).

    MATH  MathSciNet  Google Scholar 

  11. H. Minc, Permanents, Cambridge Univ. Press, Cambridge (1984).

    Book  Google Scholar 

  12. G. P’olya, “Aufgabe 424,” Arch. Math. Phys., 20, No. 3, 271 (1913)

    Google Scholar 

  13. N. Robertson, P. D. Seymour, and R. Thomas, “Permanents, Pfaffian orientations, and even directed circuits,” Ann. Math., 150, 929–975 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  14. L. G. Valiant, “The complexity of computing the permanent,” Theor. Comput. Sci., 8, 189-201 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  15. V. V. Vazirani and M. Yannakakis, “Pfaffian orientations, 0-1 permanents, and even cycles in directed graphs,” Discrete Appl. Math., 25, 179-190 (1989).

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to M. V. Budrevich.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 419, 2013, pp. 26–42.

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Budrevich, M.V. Arithmetic Matrix Operations that Preserve Conversion. J Math Sci 199, 386–393 (2014). https://doi.org/10.1007/s10958-014-1866-3

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