Maximising the permanent of (0,1)-matrices and the number of extensions of Latin rectangles

Electronic Journal of Combinatorics

Volumn 5, Issue 1, 1998, Pages

  McKay, B D ^a   Wanless, I M ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039977014     PISSN: 10778926     EISSN: None     Source Type: Journal    
DOI: 10.37236/1349     Document Type: Article

References (16)

1. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover publications, New York, 1965.
2. k, Proceedings of the All-Union Seminar on Discrete Mathematics and its Applications (Russian) ed. O. B. Lupanov, Moskov. Gos. Univ., Moscow, 1986, 65-73.
3. L. M. Brègman, Some properties of nonnegative matrices and their permanents, Soviet Math. Dokl. 14:945-949 (1973).
4. R. A. Brualdi, J. L. Goldwasser and T. S. Michael, Maximum permanents of matrices of zeroes and ones, J. Comb. Th. A 47:207-245 (1988).
5. F. R. K. Chung, P. Diaconis, R. L. Graham and C. L. Mallows, On the permanents of complements of the direct sums of identity matrices, Adv. in Appl. Math. 2:121-137 (1981).
6. C. D. Godsil, Matchings and walks in graphs, J. Graph Th. 5:285-297 (1981).
7. C. D. Godsil and B. D. McKay, Asymptotic enumeration of Latin rectangles, J. Comb. Th. B 48:19-44 (1990).
8. O. J. Heilmann and E. H. Lieb, Theory of monomer-dimer systems, Comm. Math. Physics 25:190-232 (1972).
9. S. A. Joni and G.-C. Rota, A vector space analog of permutations with restricted position, J. Comb. Th. A 29:59-73 (1980).
10. k, Linear and Multilinear Algebra 9:81-91 (1980).
11. H. Minc, Permanents, Encyclopedia Math. Appl., Addison-Wesley, Reading, Mass., 1978.
12. H. Minc, Theory of permanents 1978-1981, Linear and Multilinear Algebra 12:227-263, (1983).
13. A. Schrijver, Bounds on permanents, and the number of 1-factors and 1-factorizations of bipartite graphs, London Math. Soc. Lecture Note Ser. 82:107-134 (1983).
14. I. M. Wanless, The Holens-Doković Conjecture on permanents fails, (submitted for publication).
15. I. M. Wanless, Maximising the permanent and complementary permanent of (0,1)-matrices with constant line sum, (submitted for publication).
16. N. Zagaglia-Salvi, Permanents and determinants of circulant (0, 1)-matrices, Matematiche (Catania) 39:213-219 (1984).