Release Time:2021-03-05  Hits:

Indexed by: Journal Article

Date of Publication: 2021-03-05

Journal: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY

Volume: 63

Issue: 4

Page Number: 1062-1070

ISSN: 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.