94-26 Classification of Partition Varieties

DIMACS TR: 94-26

Classification of Partition Varieties

Author: Kequan Ding

ABSTRACT
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.

Paper available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1994/94-26.ps

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