DIMACS TR: 94-26
Classification of Partition Varieties
Author: Kequan Ding
In this paper we classify the partition varieties according to their
homology and cohomology groups. Using the results obtained in the
cellular decomposition of partition varieties in the author's thesis,
we reduced the problem into a combinatorial problem. Then we use
the theorems Proved by Foata-Schutzenberger, Garsia-Remmel and
Goldman-Joichi-White, we give a complete solution to this problem.
Our main result is that two partition variueties share the same
homology and cohomology groups if and only if their corresponding
Ferrers boards share the same diagonal data.
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