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Interpolation by polynomial functions of distributive lattices: a generalization of a theorem of R. L. Goodstein

dc.contributor.authorWaldhauser, Tamás
dc.contributor.authorCouceiro, Miguel
HAL ID: 1498
dc.date.accessioned2012-09-28T07:50:06Z
dc.date.available2012-09-28T07:50:06Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10319
dc.descriptionRéférence ArXiV indiquée ci-dessous sous le titre : "A generalization of Goodstein's theorem: interpolation by polynomial functions of distributive lattices"en
dc.language.isoenen
dc.subjectLattice polynomial functionen
dc.subjectdistributive latticeen
dc.subjectpolynomial interpolationen
dc.subjectGoodstein's theoremen
dc.subjectdisjunctive normal formen
dc.subject.ddc512en
dc.titleInterpolation by polynomial functions of distributive lattices: a generalization of a theorem of R. L. Goodsteinen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversity of Szeged;
dc.description.abstractenWe consider the problem of interpolating functions partially defined over a distributive lattice, by means of lattice polynomial functions. Goodstein's theorem solves a particular instance of this interpolation problem on a distributive lattice L with least and greatest elements 0 and 1, resp.: Given an n-ary partial function f over L, defined on all 0-1 tuples, f can be extended to a lattice polynomial function p over L if and only if f is monotone; in this case, the interpolating polynomial p is unique. We extend Goodstein's theorem to a wider class of n-ary partial functions f over a distributive lattice L, not necessarily bounded, where the domain of f is a cuboid of the form D={a1,b1}x...x{an,bn} with ai<bi, and determine the class of such partial functions which can be interpolated by lattice polynomial functions. In this wider setting, interpolating polynomials are not necessarily unique; we provide explicit descriptions of all possible lattice polynomial functions which interpolate these partial functions, when such an interpolation is available.en
dc.relation.isversionofjnlnameAlgebra Universalis
dc.relation.isversionofjnlvol69
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2013
dc.relation.isversionofjnlpages287-299
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00012-013-0231-6
dc.identifier.urlsitehttp://arxiv.org/abs/1110.0321en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAlgèbreen


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