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A natural representation of partitions as terms of a universal algebra

Part of: Varieties Algebraic structures Combinatorics

Published online by Cambridge University Press:  09 April 2009

Harry Lakser
Harry Lakser
Affiliation:
Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Canada, R3T 2N2
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Abstract

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We consider a variety of algebras with two binary commutative and associative operations. For each integer n ≥ 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.

Keywords

Bell bisemigroupessentialy n-arypartitionvariety.

MSC classification

Secondary: 08A40: Operations, polynomials, primal algebras 08B20: Free algebras 05A17: Partitions of integers
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 3 , December 1993 , pp. 311 - 324
Copyright
Copyright © Australian Mathematical Society 1993

References

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