A Bijection between Atomic Partitions and Unsplitable Partitions
Combinatorics
2011-08-08 v1
Abstract
In the study of the algebra of symmetric functions in noncommutative variables, Bergeron and Zabrocki found a free generating set consisting of power sum symmetric functions indexed by atomic partitions. On the other hand, Bergeron, Reutenauer, Rosas, and Zabrocki studied another free generating set of consisting of monomial symmetric functions indexed by unsplitable partitions. Can and Sagan raised the question of finding a bijection between atomic partitions and unsplitable partitions. In this paper, we provide such a bijection.
Cite
@article{arxiv.1009.0661,
title = {A Bijection between Atomic Partitions and Unsplitable Partitions},
author = {William Y. C. Chen and Teresa X. S. Li and David G. L. Wang},
journal= {arXiv preprint arXiv:1009.0661},
year = {2011}
}
Comments
6 pages