The excedance set of a permutation Ο = Ο 1 Ο 2 β’ β’ β’ Ο n is the set of indices i for which Ο i > i. We give a formula for the number of permutations with a given excedance set and recursive formulas satisfied by these numbers. We prove log-concavity of certain sequences of these numbers and we show
The permuted analogues of three Catalan sets
β Scribed by M.R.T. Dale; J.W. Moon
- Book ID
- 103798146
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 716 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0378-3758
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
If a sequence of transitive permutation groups G of degree n have orders which are not too large (log IGI--o(n~) suttices), then the number of orbits on the power set is asymptotically 2n/]GI, and almost all of these orbits are regular. This conclusion holds in particular for primitive groups.
Three main semantics for membership functions seem to exist in the literature: similarity, preference and uncertainty. Each semantics underlies a particular class of applications. Similarity notions are exploited in clustering analysis and fuzzy controllers. Uncertainty is captured by fuzzy sets in
## Dedicated to G. Zappa on his 70th birthday \* Research done within the activity of GNSAGA of CNR, supported by the 40% grants of MPI.