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{\bf William Y. C. Chen, Teresa X. S. Li and David G. L. Wang}
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{\bf A Bijection between Atomic Partitions and Unsplitable Partitions}
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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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