Adjacent q-cycles 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 e-prints
- Pub Date:
- May 2010
- DOI:
- 10.48550/arXiv.1005.0781
- arXiv:
- arXiv:1005.0781
- Bibcode:
- 2010arXiv1005.0781B
- Keywords:
-
- Mathematics - Combinatorics;
- 05A05;
- 05A10;
- 05A15
- E-Print:
- 14 pages