Balanced Properties of the q-Derangement Numbers and the q-Catalan Numbers
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🧮 math.CO
keywords
balancednumberspropertyq-catalanq-derangementbonaconditioncriterion
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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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