GENERALIZATIONS OF DYSON'S RANK (COMBINATORIAL, PARTITIONS, CONGRUENCES).
- Author
- GARVAN, FRANCIS GERARD
- Physical Description
- 136 pages
- Additional Creators
- Pennsylvania State University
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- Summary
- In this thesis we find combinatorial interpretations of congruence results for partitions and other related combinatorial objects. Our combinatorial interpretations are analogous to Dyson's 'rank' results for partitions modulo 5 and 7.
In particular we find 'rank-type' results, for what we call vector partitions, which are new combinatorial interpretations for the classical congruences for partitions modulo 5, 7, and 11. The existence of such a result modulo 11 was first conjectured by Dyson.
We also find a 'rank-type' result for generalized Frobenius partitions. The existence of such a result was conjectured by Andrews who discovered and proved the corresponding congruence result modulo 5. We also find new analytic and combinatorial results for colored and uncolored generalized Frobenius partitions.
Finally we find the correct ranks for two- and three-line partitions which were asked for by Atkin. These ranks yield combinatorial interpretations of Gordon and Cheema's congruence results modulo 3 and 5. - Other Subject(s)
- Dissertation Note
- Ph.D. The Pennsylvania State University 1986.
- Note
- Source: Dissertation Abstracts International, Volume: 47-04, Section: B, page: 1586.
- Part Of
- Dissertation Abstracts International
47-04B
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