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CONTENT AND SINGLETONS BRING UNIQUE IDENTIFICATION MINORS

Part of: Ordered sets Algebraic structures

Published online by Cambridge University Press:  29 October 2018

ERKKO LEHTONEN Open the ORCID record for ERKKO LEHTONEN [Opens in a new window]
ERKKO LEHTONEN*
Affiliation:
Technische Universität Dresden, Institut für Algebra, 01062 Dresden, Germany email [email protected]
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Abstract

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A new class of functions with a unique identification minor is introduced: functions determined by content and singletons. Relationships between this class and other known classes of functions with a unique identification minor are investigated. Some properties of functions determined by content and singletons are established, especially concerning invariance groups and similarity.

Keywords

function of several argumentsidentification minorinvariance grouppermutation pattern

MSC classification

Primary: 08A40: Operations, polynomials, primal algebras
Secondary: 06A07: Combinatorics of partially ordered sets
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 107 , Issue 1 , August 2019 , pp. 67 - 90
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Berman, J. and Kisielewicz, A., ‘On the number of operations in a clone’, Proc. Amer. Math. Soc. 122 (1994), 359–369.Google Scholar
Bóna, M., Combinatorics of Permutations, Discrete Mathematics and Applications (Chapman & Hall/CRC, Boca Raton, FL, 2004).Google Scholar
Bouaziz, M., Couceiro, M. and Pouzet, M., ‘Join-irreducible Boolean functions’, Order 27 (2010), 261–282.Google Scholar
Couceiro, M. and Foldes, S., ‘On closed sets of relational constraints and classes of functions closed under variable substitutions’, Algebra Universalis 54 (2005), 149–165.Google Scholar
Couceiro, M., Lehtonen, E. and Schölzel, K., ‘A complete classification of equational classes of threshold functions included in clones’, RAIRO Oper. Res. 49 (2015), 39–66.Google Scholar
Couceiro, M., Lehtonen, E. and Schölzel, K., ‘Set-reconstructibility of Post classes’, Discrete Appl. Math. 187 (2015), 12–18.Google Scholar
Couceiro, M., Lehtonen, E. and Schölzel, K., ‘Hypomorphic Sperner systems and non-reconstructible functions’, Order 32 (2015), 255–292.Google Scholar
Ekin, O., Foldes, S., Hammer, P. L. and Hellerstein, L., ‘Equational characterizations of Boolean function classes’, Discrete Math. 211 (2000), 27–51.Google Scholar
Grech, M. and Kisielewicz, A., ‘Symmetry groups of Boolean functions’, European J. Combin. 40 (2014), 1–10.Google Scholar
Horváth, E. K., Makay, G., Pöschel, R. and Waldhauser, T., ‘Invariance groups of finite functions and orbit equivalence of permutation groups’, Open Math. 13 (2015), 83–95.Google Scholar
Kisielewicz, A., ‘Symmetry groups of Boolean functions and constructions of permutation groups’, J. Algebra 199 (1998), 379–403.Google Scholar
Kitaev, S., Patterns in Permutations and Words, Monogr. Theoret. Comput. Sci. EATCS Ser. (Springer, Heidelberg, 2011).Google Scholar
Lehtonen, E., ‘Totally symmetric functions are reconstructible from identification minors’, Electron. J. Combin. 21(2) (2014), P2.6.Google Scholar
Lehtonen, E., ‘Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings’, Internat. J. Algebra Comput. 24 (2014), 11–31.Google Scholar
Lehtonen, E., ‘On functions with a unique identification minor’, Order 33 (2016), 71–80.Google Scholar
Lehtonen, E., ‘Permutation groups arising from pattern involvement’, Preprint, 2016, arXiv:1605.05571v3.Google Scholar
Lehtonen, E. and Pöschel, R., ‘Permutation groups, pattern involvement, and Galois connections’, Acta Sci. Math. (Szeged) 83 (2017), 355–375.Google Scholar
Pippenger, N., ‘Galois theory for minors of finite functions’, Discrete Math. 254 (2002), 405–419.Google Scholar
Willard, R., ‘Essential arities of term operations in finite algebras’, Discrete Math. 149 (1996), 239–259.Google Scholar
Zverovich, I. E., ‘Characterizations of closed classes of Boolean functions in terms of forbidden subfunctions and Post classes’, Discrete Appl. Math. 149 (2005), 200–218.Google Scholar