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Asymptotic normality in t-stack sortable permutations

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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… Click to show full abstract

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: asymptotic normality; stack sortable; sortable permutations; normality stack

Journal Title: Proceedings of the Edinburgh Mathematical Society
Year Published: 2020

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