Model
Digital Document
Publisher
Florida Atlantic University
Description
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.
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.
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