On a constructive approach to the calculation of cardinality of the Ryser classes. (English. Russian original) Zbl 1237.05126
Discrete Math. Appl. 19, No. 4, 371-374 (2009); translation from Diskretn. Mat. 21, No. 3, 33-36 (2009).
Summary: We consider the problem of calculation of cardinality of the classes of square matrices consisting of zeros and ones with given values of row and column sums. We obtain a recurrence relation which gives a possibility to calculate the cardinalities of these classes. In the proofs, we use a constructive approach, that is, we construct the combinatorial objects with given characteristics and calculate the number of distinct objects. An example of the use of the obtained relation is given.
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
References:
| [1] | Gale D., Pacific J. Math. 7 pp 1073– (1957) |
| [2] | Ryser H. J., Canadian J. Math. 9 pp 371– (1957) · Zbl 0079.01102 · doi:10.4153/CJM-1957-044-3 |
| [3] | Wang B. Y., Discrete Math. 187 pp 211– (1998) · Zbl 0957.05023 · doi:10.1016/S0012-365X(97)00197-0 |
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