On colored set partitions of type B n

David Wang

Open Mathematics (2014)

  • Volume: 12, Issue: 9, page 1372-1381
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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David Wang. "On colored set partitions of type B n." Open Mathematics 12.9 (2014): 1372-1381. <http://eudml.org/doc/269733>.

@article{DavidWang2014,
abstract = {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.},
author = {David Wang},
journal = {Open Mathematics},
keywords = {Set partition; Limiting distribution; set partition; limiting distribution},
language = {eng},
number = {9},
pages = {1372-1381},
title = {On colored set partitions of type B n},
url = {http://eudml.org/doc/269733},
volume = {12},
year = {2014},
}

TY - JOUR
AU - David Wang
TI - On colored set partitions of type B n
JO - Open Mathematics
PY - 2014
VL - 12
IS - 9
SP - 1372
EP - 1381
AB - 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.
LA - eng
KW - Set partition; Limiting distribution; set partition; limiting distribution
UR - http://eudml.org/doc/269733
ER -

References

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