2 research outputs found
A Bijection between Atomic Partitions and Unsplitable Partitions
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.Comment: 6 page