Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-13T09:18:04.248Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Dudek, J., ‘A characterization of distributive lattices’, in: Contributions to Lattice Theory (Szeged 1980), volume 33 of Colloq. Math. Soc. J´nos Bolyai (North-Holland, Amsterdam, 1983) pp. 325–335.Google Scholar
[2]Grätzer, G., ‘Composition of functions’, in: Proceedings of the Conference on Universal Algebra, October 1969 (ed. Wenzel, G. H.), Queen's Papers in Pure and Applied Mathematics (Queen's University, Kingston, 1970) pp. 1–106.Google Scholar
[3]Kisielewicz, A., ‘Characterization of pn-sequences for nonidempotent algebras’, J. of Algebra 108 (1987), 102–115.CrossRefGoogle Scholar
[4]McKenzie, R. N., McNulty, G. F. and Taylor, W. F, in: Algebras, Lattices, Varieties Volume I, The Wadsworth & Brooks/Cole Mathematics Series (Wadsworth & Brooks/Cole, Monterey, 1987).Google Scholar
[5]Stanley, R. P., in: Enumerative Combinatorics Volume I, The Wadsworth & Brooks/Cole Mathematics Series (Wadsworth & Brooks/Cole, Monterey, 1986).CrossRefGoogle Scholar