Conversion of the permanent into the determinant
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- by P. M. Gibson
- Proc. Amer. Math. Soc. 27 (1971), 471-476
- DOI: https://doi.org/10.1090/S0002-9939-1971-0279110-X
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Abstract:
Let $A$ be an $n$-square $(0,1)$-matrix with positive permanent. It is shown that if the permanent of $A$ can be converted into a determinant by affixing $\pm$ signs to the elements of $A$ then $A$ has at most $({n^2} + 3n - 2)/2$ positive entries. Corollaries of this result are given.References
- P. M. Gibson, An identity between permanents and determinants, Amer. Math. Monthly 76 (1969), 270–271. MR 241439, DOI 10.2307/2316368
- Marvin Marcus and Henryk Minc, On the relation between the determinant and the permanent, Illinois J. Math. 5 (1961), 376–381. MR 147488
- Henryk Minc, On lower bounds for permanents of $(0,\,1)$ matrices, Proc. Amer. Math. Soc. 22 (1969), 117–123. MR 245585, DOI 10.1090/S0002-9939-1969-0245585-6 G. Pólya, Aufgabe 424, Arch. Math. Phys. (3) 20 (1913), 271.
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 471-476
- MSC: Primary 15.20
- DOI: https://doi.org/10.1090/S0002-9939-1971-0279110-X
- MathSciNet review: 0279110