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A Canonical Form For Fully Indecomposable (0,1)-Matrices

Published online by Cambridge University Press:  20 November 2018

D. J. Hartfiel
D. J. Hartfiel*
Affiliation:
Mathematics Department, Texas A & M University, College Station, Texas 77843
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This paper develops another canonical form for (0, 1)-matrices which may be used in the same spirit as the nearly decomposable matrix [5] or the k-nearly decomposable matrix [1], This form is intrinsic in each fully indecomposable matrix and does not require the replacement of any of its non-zero entries by 0's.

Keywords

Primary 1530Secondary 1548(0, 1)-matricespermanentlower bounds
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 223 - 227
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Hartfiel, D. J. and Crosby, J. W., A lower bound for the permanent on Unk, k), Journal of Combinatorial Theory, Vol. 12 No. 2, (1972), 283-288.Google Scholar
2. Hartfiel, D. J. and Crosby, J. W., On the permanent of a certain class of(0, l)-matrices, Canadian Bulletin, Vol. 14 No. 4, (1971), 507-511.Google Scholar
3. Marcus, Marvin and Newman, Morris, On the minimum of the permanent of a doubly stochastic matrix.Duke Mathematical Journal, 26 (1959), 61-72.Google Scholar
4. Mine, H., On lower bounds for permanent of (0, 1)-matrices, Proceedings of the American Mathematical Society, 22 (1969), 117-123.Google Scholar
5. Sinkhorn, Richard and Knopp, Paul, Problems involving diagonal products in non-negative matrices, Transactions of the American Mathematical Society, 136 (1969), 67-75.Google Scholar