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.
@article{bwmeta1.element.doi-10_2478_s11533-014-0419-9,
author = {David Wang},
title = {On colored set partitions of type B n},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1372-1381},
zbl = {1292.05049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0419-9}
}
David Wang. On colored set partitions of type B n. Open Mathematics, Tome 12 (2014) pp. 1372-1381. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0419-9/
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