http://dx.doi.org/10.1007/s00026-011-0113-6">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Counting simsun permutations by descents

Language

English

Abstract

We count in the present work simsun permutations of length n by their number of descents. Properties studied include the recurrence relation and real-rootedness of the generating function of the number of n-simsun permutations with k descents. By means of generating function arguments, we show that the descent number is equidistributed over n-simsun permutations and n-André permutations. We also compute the mean and variance of the random variable Xn taking values the descent number of random n-simsun permutations, and deduce that the distribution of descents over random simsun permutations of length n satisfies a central and a local limit theorem as n → + ∞. © 2011 Springer Basel AG.

Keywords

André trees, asymptotically normal, descents, simsun permutations

Publication Date

2011

Source Publication Title

Annals of Combinatorics

Volume

15

Issue

4

Start Page

625

End Page

635

Publisher

Springer Verlag

ISSN (print)

02180006

ISSN (electronic)

02193094

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