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 → + ∞. Copyright © 2011 Springer Basel AG.
CitationChow, C.-O., & Shiu, W. C. (2011). Counting simsun permutations by descents. Annals of Combinatorics, 15(4), 625-635.
- Simsun permutations
- Andr´e trees
- Asymptotically normal