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

Waldhauser, Tamás; Couceiro, Miguel (2013), Interpolation by polynomial functions of distributive lattices: a generalization of a theorem of R. L. Goodstein, Algebra Universalis, 69, 3, p. 287-299. http://dx.doi.org/10.1007/s00012-013-0231-6

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1110.0321
Date
2013
Journal name
Algebra Universalis
Volume
69
Number
3
Publisher
Springer
Pages
287-299
Publication identifier
http://dx.doi.org/10.1007/s00012-013-0231-6
Metadata
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Author(s)
Waldhauser, Tamás
Couceiro, Miguel
Abstract (EN)
We 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
Subjects / Keywords
Lattice polynomial function; distributive lattice; polynomial interpolation; Goodstein's theorem; disjunctive normal form

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