We introduce an operator on permutations of 1, 2, . . . , n, which preserves the numbers of their ascents and descents. We investigate periods of permutations under the operator and structures of permutations with given periods. As its application we prove some congruence relations modulo a prime fo
On the Numbers of Orbits of Permutations under an Operator Related to Eulerian Numbers
β Scribed by Shinji Tanimoto
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 191 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0218-0006
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π SIMILAR VOLUMES
Eulerian and Simon Newcomb numbers are two of the most celebrated numbers associated with random permutations. Their distributions have been successfully used in various areas of statistics and applied probability. Conventionally, these distributions have been studied via combinatorial analysis. In
The main purpose of this paper is to give some natural relations between the entropy numbers of an operator and those of its adjoint. This problem has attracted some recent attention (of. [ll], 14.3. 6 and[a]). Typically, we shall consider inequalities which allow a correction term. We obtain our fi