New permutation statistics: Variation and a variant

Toufik Mansour, Chunwei Song

Research output: Contribution to journalArticlepeer-review


For each permutation π we introduce the variation statistic of π, as the total number of elements on the right between each two adjacent elements of π. 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.

Original languageEnglish
Pages (from-to)1974-1978
Number of pages5
JournalDiscrete Applied Mathematics
Issue number8
StatePublished - 28 Apr 2009

Bibliographical note

Funding Information:
The second author’s work was partially supported by the National Science Foundation of China (Grant No. 10726011).


  • Generating functions
  • Kernel method
  • Mahonian
  • Permutation statistics
  • Variation statistic

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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