Counting Simsun Permutations by Descents

Chak On Chow*, Wai Chee SHIU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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 → + ∞.

Original languageEnglish
Pages (from-to)625-635
Number of pages11
JournalAnnals of Combinatorics
Volume15
Issue number4
DOIs
Publication statusPublished - Oct 2011

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics

User-Defined Keywords

  • André trees
  • asymptotically normal
  • descents
  • simsun permutations

Fingerprint

Dive into the research topics of 'Counting Simsun Permutations by Descents'. Together they form a unique fingerprint.

Cite this