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arXiv · 1009.0661

A Bijection between Atomic Partitions and Unsplitable Partitions

William Y. C. Chen·Teresa X. S. Li·David G. L. Wang
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Abstract

In the study of the algebra $\mathrm{NCSym}$ 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 $\mathrm{NCSym}$ 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.

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William Y. C. Chen, Teresa X. S. Li, David G. L. Wang. 2010-09-03. A Bijection between Atomic Partitions and Unsplitable Partitions. https://arxiv.org/abs/1009.0661

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