Balanced Properties of the q-Derangement Numbers and the q-Catalan Numbers

Details Balanced Properties of the q-Derangement Numbers and the q-Catalan Numbers Balanced Properties of the q-Derangement Numbers and the q-Catalan Numbers

2009-11-16

arxiv.org/abs/0911.2935v1

Mathematics

Combinatorics

9 pages

Scientific paper

Based on Bona's condition for the balanced property of the number of cycles
of permutations, we give a general criterion for the balanced property in terms
of the generating function of a statistic. We show that the q-derangement
numbers and the q-Catalan numbers satisfy the balanced property.

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