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arXiv · 1005.0781

Adjacent q-cycles in permutations

Richard A. Brualdi·Emeric Deutsch
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Abstract

We introduce a new permutation statistic, namely, the number of cycles of length $q$ consisting of consecutive integers, and consider the distribution of this statistic among the permutations of $\{1,2,...,n\}$. We determine explicit formulas, recurrence relations, and ordinary and exponential generating functions. A generalization to more than one fixed length is also considered.

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Richard A. Brualdi, Emeric Deutsch. 2010-05-13. Adjacent q-cycles in permutations. https://arxiv.org/abs/1005.0781

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