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Asymptotic normality in t-stack sortable permutations

Part of: Limit theorems Combinatorics Distribution theory

Published online by Cambridge University Press:  04 November 2020

Xi Chen ,
Jianxi Mao  and
Yi Wang
Xi Chen
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Dalian116024, PR China (wangyi@dlut.edu.cn)
Jianxi Mao
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Dalian116024, PR China (wangyi@dlut.edu.cn)
Yi Wang
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Dalian116024, PR China (wangyi@dlut.edu.cn)
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Abstract

In this paper, we show that the numbers of t-stack sortable n-permutations with k − 1 descents satisfy central and local limit theorems for t = 1, 2, n − 1 and n − 2. This result, in particular, gives an affirmative answer to Shapiro's question about the asymptotic normality of the Narayana numbers.

Keywords

Narayana numberst-stack sortable permutationsasymptotic normalitycentral limit theoremlocal limit theorem

MSC classification

Primary: 05A10: Factorials, binomial coefficients, combinatorial functions
Secondary: 60F05: Central limit and other weak theorems 62E20: Asymptotic distribution theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 4 , November 2020 , pp. 1062 - 1070
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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