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Number of Permutations with Prescribed Up-Down Structure as a Function of Two Variables

Vladimir Shevelev
Published Online: 2012-08-01 | DOI: https://doi.org/10.1515/integers-2011-0122


We consider the number of permutations with prescribed up-down structure as a function of two arguments: the number n of elements and the introduced up-down index k of a permutation. We consider sets of permutations for which k is a fixed number and when k is a function of n. In the first case the number of permutations is a polynomial in n, the degree of which is defined by k.

Keywords: Alternating Permutations; Eulerian Numbers; Niven's Signature for Permutations

About the article

Received: 2010-09-27

Revised: 2011-06-30

Accepted: 2011-11-20

Published Online: 2012-08-01

Published in Print: 2012-08-01

Citation Information: Integers, Volume 12, Issue 4, Pages 529–569, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2011-0122.

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