Adjacent qcycles in permutations
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.
 Publication:

arXiv eprints
 Pub Date:
 May 2010
 DOI:
 10.48550/arXiv.1005.0781
 arXiv:
 arXiv:1005.0781
 Bibcode:
 2010arXiv1005.0781B
 Keywords:

 Mathematics  Combinatorics;
 05A05;
 05A10;
 05A15
 EPrint:
 14 pages