A lower bound for the permanent of a $(0, 1)$-matrix
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- by P. M. Gibson PDF
- Proc. Amer. Math. Soc. 33 (1972), 245-246 Request permission
Abstract:
Let $A = ({a_{ij}})$ be an n-square fully indecomposable $(0,1)$-matrix. It is shown that if each row sum of A is at least k then per $A \geqq \sum \nolimits _{i,j = 1}^n{a_{ij}} - 2n + 2 + \sum \nolimits _{m = 1}^{k - 1}(m! - 1)$. This improves an inequality obtained by H. Minc.References
- Marshall Hall Jr., Distinct representatives of subsets, Bull. Amer. Math. Soc. 54 (1948), 922–926. MR 27033, DOI 10.1090/S0002-9904-1948-09098-X
- D. J. Hartfiel, A simplified form for nearly reducible and nearly decomposable matrices, Proc. Amer. Math. Soc. 24 (1970), 388–393. MR 252415, DOI 10.1090/S0002-9939-1970-0252415-3
- 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
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 245-246
- MSC: Primary 15A15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294360-5
- MathSciNet review: 0294360