Geodesic
A bijection between atomic partitions and unsplitable partitions
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/494
Classification : 05A18, 05A19, 05E05
Mots-clés : symmetric functions, noncommutative variables 
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     year = {2011},
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William Y. C. Chen; Teresa X. S. Li; David G. L. Wang. A bijection between atomic partitions and unsplitable partitions. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/494

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