Note: New permutation statistics: Variation and a variant

Authors:
Toufik Mansour;Chunwei Song
Affiliations:
Department of Mathematics, University of Haifa, 31905 Haifa, Israel;School of Mathematical Sciences, LMAM, Peking University, Beijing 100871, PR China
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 4
Cited 0

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Abstract

For each permutation @p we introduce the variation statistic of @p, as the total number of elements on the right between each two adjacent elements of @p. We modify this new statistic to get a slightly different variant, which behaves more closely like Mahonian statistics such as maj. In this paper we find an explicit formula for the generating function for the number of permutations of length n according to the variation statistic, and for that according to the modified version.