The Limiting Distribution of the Number of Block Pairs in Type B Set Partitions

2011/08/05 by David G. L. Wang, Wang, David G. L.
Mathematics · #05A18 #60C05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1108.1264

openalex publication_date 2011/08/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

It is a classical result of Harper that the limiting distribution of the number of blocks in partitions of the set \1, 2,..., n\ is normal. In this paper, using the saddle point method we prove the normality of the limiting distribution of the number of block pairs in set partitions of type B_n. Moreover, we obtain that the limiting distribution of the number of block pairs in B_n-partitions without zero-block is also normal.

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