Adjacent q-cycles in permutations
Richard A. Brualdi, Emeric Deutsch · arXiv (Cornell University) · 2010
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.