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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In memory of our friend Miki Neumann (1946–2011)
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Brualdi, R.A., Deutsch, E. Adjacent q-Cycles in Permutations. Ann. Comb. 16, 203–213 (2012). https://doi.org/10.1007/s00026-012-0126-9
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DOI: https://doi.org/10.1007/s00026-012-0126-9