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{\bf Sarah Iveson}
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{\bf Inversions Within Restricted Fillings of Young Tableaux}
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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.
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