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A Bijection between Atomic Partitions and Unsplitable Partitions
Bijection Atomic Partitions Unsplitable Partitions
2014/6/3
In the study of the algebra NCSym of symmetric functions in noncommutative variables, Bergeron and Zabrocki found a free generating set consisting of power sum symmetric functions indexed by atomic pa...
A Bijection between Atomic Partitions and Unsplitable Partitions
Bijection between Atomic Partitions Unsplitable Partitions
2010/11/29
In the study of the algebra NCSym of symmetric functions in noncommutative variables, Bergeron and Zabrocki found a free generating set consisting of power sum symmetric functions indexed by atomic pa...
Han's Bijection via Permutation Codes
Foata's second transformation Mahonian statistic cyclic major code cyclic inversion code partial Foata map
2014/6/3
We show that Han’s bijection when restricted to permutations can be carried out in terms of the cyclic major code and the cyclic inversion code. In other words, it maps a permutation π with cyclic maj...
Adjacency Preserving Bijection Maps of Hermitian Matrices over any Division Ring with an Involution
division ring with involution hermitian matrix adjacency geometry of matrices
2007/12/11
Let $D$ be any division ring with an involution, ${\mathscr H}_n(D)$ be the space of all $n\times n$ hermitian matrices over $D$. Two hermitian matrices $A$ and $B$ are said to be adjacent if ${\rm ra...