Geodesic
On a~constructive approach to the calculation of cardinality of the Ryser classes
Diskretnaya Matematika, Tome 21 (2009) no. 3, pp. 33-36

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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. 
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     author = {V. S. Krotkin and O. V. Kuzmin},
     title = {On a~constructive approach to the calculation of cardinality of the {Ryser} classes},
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V. S. Krotkin; O. V. Kuzmin. On a~constructive approach to the calculation of cardinality of the Ryser classes. Diskretnaya Matematika, Tome 21 (2009) no. 3, pp. 33-36. http://geodesic.mathdoc.fr/item/DM_2009_21_3_a3/