J Austral Math Soc Ser A 55 pp311--324, 1993.

A Natural Representation of Partitions as Terms of a Universal Algebra

Harry Lakser

Abstract

We consider a variety of algebras with two binary commutative and associative operations. For each integer n ³ 0, we represent the partitions on an n-element set as n-ary terms in the variety. We determine necessary and sufficient conditions on the variety ensuring that, for each n, these representing terms be all the essentially n-ary terms and moreover that distinct partitions yield distinct terms.

1991 AMS Subject Classification: primary 08A40 secondary 08B20, 05A17

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Authors

Harry Lakser

Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2.