Counting Simsun Permutations by Descents

Chak-On Chow*, Wai Chee Shiu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

13 Citations (Scopus)
18 Downloads (Pure)


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
Issue number4
Publication statusPublished - Oct 2011

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics

User-Defined Keywords

  • André trees
  • asymptotically normal
  • descents
  • simsun permutations


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