Geodesic
Partitions, Kostka polynomials and pairs of trees
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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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 
@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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Eliana Zoque. Partitions, Kostka polynomials and pairs of trees. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/18

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