Geodesic
Partitions, Kostka polynomials and pairs of trees
The electronic journal of combinatorics, Tome 19 (2012) no. 1

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Zbl arXiv
Bennett et al. presented a recursive algorithm to create a family of partitions from one or several partitions. They were mainly interested in the cases when we begin with a single square partition or with several partitions with only one part. The cardinalities of those families of partitions are the Catalan and ballot numbers, respectively. In this paper we present a non-recursive description for those families and prove that the generating function of the size of those partitions is a Kostka number. We also present bijections between those sets of partitions and sets of trees and forests enumerated by the Catalan an ballot numbers, respectively.
DOI : 10.37236/18
Classification : 05A17, 17B15, 05E05
Mots-clés : Catalan numbers, Kostka number, ballot numbers, symmetric functions, finite dimensional representation of Lie algebras 
Eliana Zoque. Partitions, Kostka polynomials and pairs of trees. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/18
@article{10_37236_18,
     author = {Eliana Zoque},
     title = {Partitions, {Kostka} polynomials and pairs of trees},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/18},
     zbl = {1244.05232},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/18/}
}
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