Geodesic
Inversions within restricted fillings of Young tableaux
The electronic journal of combinatorics, Tome 13 (2006)
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In this paper we study inversions within restricted fillings of Young tableaux. These restricted fillings are of interest because they describe geometric properties of certain subvarieties, called Hessenberg varieties, of flag varieties. We give answers and partial answers to some conjectures posed by Tymoczko. In particular, we find the number of components of these varieties, give an upper bound on the dimensions of the varieties, and give an exact expression for the dimension in some special cases. The proofs given are all combinatorial.
DOI : 10.37236/1030
Classification : 05E10, 14M15
Mots-clés : Hessenberg varieties 
@article{10_37236_1030,
     author = {Sarah Iveson},
     title = {Inversions within restricted fillings of {Young} tableaux},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1030},
     zbl = {1080.05099},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1030/}
}
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Sarah Iveson. Inversions within restricted fillings of Young tableaux. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1030

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