Adjacent q-cycles in permutations

Details Adjacent q-cycles in permutations Adjacent q-cycles in permutations

2010-05-05

arxiv.org/abs/1005.0781v2

Mathematics

Combinatorics

14 pages

Scientific paper

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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