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Indexed by:期刊论文

Date of Publication:2021-03-05

Journal:PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY

Volume:63

Issue:4

Page Number:1062-1070

ISSN No.:0013-0915

Key Words:Narayana numbers; t-stack sortable permutations; asymptotic normality; central limit theorem; local limit theorem

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.