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Actions and identities on set partitions
Actions and identities set partitions Combinatorics
2011/9/16
Abstract: A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero elements of an abelian group $A$. Inspired by the action of the linear characters of the unitria...
Singletons and Adjacencies of Set Partitions of Type B
set partition of type B singleton adjacency symmetric distributions
2014/6/3
We show that the joint distribution of the number of singleton pairs and the number of adjacency pairs is symmetric over the set partitions of type Bn without zero-block, in analogy with the result of...
Minimally Intersecting Set Partitions of Type B
minimally intersecting Bn-partitions Dobinski's formula the Dowling number
2014/6/3
Motivated by Pittel's study of minimally intersecting set partitions, we investigate minimally intersecting set partitions of type B. We find a formula for the number of minimally intersecting r-tuple...
A Major Index for Matchings and Set Partitions
tangled-diagram partition matching crossing nesting vacillating tableau
2014/6/3
A tangled diagram on [n] = {1,..., n} is a labeled graph for which each vertex has degree at most two. The vertices are arranged in increasing order on a horizontal line and the arcs are drawn in the ...
A Major Index for Matchings and Set Partitions
tangled-diagram partition matching crossing nesting vacillating tableau
2014/6/3
A tangled diagram on [n] = {1,..., n} is a labeled graph for which each vertex has degree at most two. The vertices are arranged in increasing order on a horizontal line and the arcs are drawn in the ...