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Title

Bijections for partition identities.

Creator

Lai, JinMei Jeng, Florida Atlantic University, Meyerowitz, Aaron, Charles E. Schmidt College of Science, Department of Mathematical Sciences

Abstract/Description

This paper surveys work of the last few years on construction of bijections for partition identities. We use the more general setting of sieveequivalent 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...
Show moreThis paper surveys work of the last few years on construction of bijections for partition identities. We use the more general setting of sieveequivalent 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.
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Date Issued

1992

PURL

http://purl.flvc.org/fau/fd/FADT14826

Subject Headings

Algorithms, Partitions (Mathematics), Sieves (Mathematics)

Format

Document (PDF)