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Bijections for partition identities

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Date Issued:
1992
Summary:
This paper surveys work of the last few years on construction of bijections for partition identities. We use the more general setting of sieve--equivalent families. Suppose A1' ... ,An are subsets of a finite set A and B1' ... ,Bn are subsets of a finite set B. Define AS=∩(i∈S) Ai and BS = ∩ (i∈S) Bi for all S⊆N={1,...,n}. Given explicit bijections fS: AS->BS for each S⊆N, A-∪Ai has the same size as B-∪Bi. Several authors have given algorithms for producing an explicit bijection between these two sets. In certain important cases they give the same result. We discuss and compare algorithms, use Graph Theory to illustrate them, and provide PAS CAL programs for them.
Title: Bijections for partition identities.
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Name(s): Lai, Jin-Mei Jeng
Florida Atlantic University, Degree grantor
Meyerowitz, Aaron, Thesis advisor
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 1992
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, FL
Physical Form: application/pdf
Extent: 38 p.
Language(s): English
Summary: This paper surveys work of the last few years on construction of bijections for partition identities. We use the more general setting of sieve--equivalent families. Suppose A1' ... ,An are subsets of a finite set A and B1' ... ,Bn are subsets of a finite set B. Define AS=∩(i∈S) Ai and BS = ∩ (i∈S) Bi for all S⊆N={1,...,n}. Given explicit bijections fS: AS->BS for each S⊆N, A-∪Ai has the same size as B-∪Bi. Several authors have given algorithms for producing an explicit bijection between these two sets. In certain important cases they give the same result. We discuss and compare algorithms, use Graph Theory to illustrate them, and provide PAS CAL programs for them.
Identifier: 14826 (digitool), FADT14826 (IID), fau:11614 (fedora)
Degree granted: Thesis (M.S.)--Florida Atlantic University, 1992.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Charles E. Schmidt College of Science
Subject(s): Algorithms
Partitions (Mathematics)
Sieves (Mathematics)
Held by: Florida Atlantic University Libraries
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FADT14826
Sublocation: Digital Library
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Owner Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.