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An Operator on Permutations and its Application to Eulerian Numbers

✍ Scribed by Shinji Tanimoto

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
87 KB
Volume
22
Category
Article
ISSN
0195-6698

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✦ Synopsis

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 for Eulerian numbers.

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