On Minc's sixth Conjecture

Abstract

Let denote the set of n × n binary matrices which have each row and column sum equal to k. Minc's Conjecture 6 asserts that is monotone decreasing in k. Here, three special cases of this conjecture and also of the corresponding statement for the maximum permanent in are proved. The three cases are for matrices which are sufficiently (i) small, (ii) sparse or (iii) dense.

Keywords:

• Permanent
• Binary matrix
• Minc conjecture

Keywords:

• Mathematics Subject Classification: 15A15

Acknowledgements

Research supported by the Australian Research Council.

Notes

†Written while the author was employed by the Department of Computer Science at the Australian National University.

Additional information

Notes on contributors

Ian M. Wanless†

†Written while the author was employed by the Department of Computer Science at the Australian National University.