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Closed classes of functions, generalized constraints, and clusters

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Abstract

Classes of functions of several variables on arbitrary nonempty domains that are closed under permutation of variables and addition of dummy variables are characterized by generalized constraints, and hereby Hellerstein’s Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary nonempty domains that are closed under permutation of variables, addition of dummy variables, and composition are characterized by clusters, and a Galois connection is established between operations and clusters.

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Author notes

  1. Erkko Lehtonen

    Present address: Université du Luxembourg, Faculté des Sciences, de la Technologie et de la Communication, 6, rue Richard Coudenhove-Kalergi, L-1359, Luxembourg, Luxembourg

Authors and Affiliations

  1. Department of Mathematics, Tampere University of Technology, P.O. Box 553, FI-33101, Tampere, Finland

    Erkko Lehtonen

  2. Department of Combinatorics and Optimization, University of Waterloo, 200 UniversityAvenue West, Waterloo, Ontario, N2L 3G1, Canada

    Erkko Lehtonen

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  1. Erkko Lehtonen
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Correspondence to Erkko Lehtonen.

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Presented by R. Pöschel.

This research was supported by the Academy of Finland, grant #120307.

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Lehtonen, E. Closed classes of functions, generalized constraints, and clusters. Algebra Univers. 63, 203–234 (2010). https://doi.org/10.1007/s00012-010-0071-6

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  • DOI: https://doi.org/10.1007/s00012-010-0071-6

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