✦ LIBER ✦
Using Recurrence Relations to Count Certain Elements in Symmetric Groups
✍ Scribed by S.P. Glasby
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 94 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
✦ Synopsis
We use the fact that certain cosets of the stabilizer of points are pairwise conjugate in a symmetric group S n in order to construct recurrence relations for enumerating certain subsets of S n . Occasionally one can find 'closed form' solutions to such recurrence relations. For example, the probability that a random element of S n has no cycle of length divisible by q is n/q d=1 (1 -1 dq ).