Geodesic
Cardinality of the Ryser Classes and the Motzkin Paths with Weights
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 3, pp. 312-318

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We consider the problem of computation of the cardinality of matrix classes with fixed row and column sums. We obtain a new recurrence formula for the cardinality of these classes which gives a connection between this problem and the Motzkin paths. Examples of using the obtained recurrence relation are furnished.
Mots-clés : (0,1)-matrix
Keywords: the Ryser classes, the Motzkin paths. 
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Vladislav S. Krotkin; Oleg V. Kuzmin. Cardinality of the Ryser Classes and the Motzkin Paths with Weights. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 3, pp. 312-318. http://geodesic.mathdoc.fr/item/JSFU_2009_2_3_a6/