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On colored set partitions of type B n

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Wang D.

Open Mathematics

2014

tom 12

nr 9

1372-1381

Generalizing Reiner’s notion of set partitions of type B n, we define colored B n-partitions by coloring the elements in and not in the zero-block respectively. Considering the generating function of colored B n-partitions, we get the exact formulas for the expectation and variance of the number of non-zero-blocks in a random colored B n-partition. We find an asymptotic expression of the total number of colored B n-partitions up to an error of O(n −1/2log7/2 n], and prove that the centralized and normalized number of non-zero-blocks is asymptotic normal over colored B n-partitions.

Ograniczanie wyników

1 Open Mathematics

1 Wang D.

1 2014

Wyniki wyszukiwania

On colored set partitions of type B n