Higman's Theorem on Discrete Sets

Authors:
Fabio Burderi;Giuseppa Castiglione;Antonio Restivo
Affiliations:
Dipartimento di Matematica e Applicazioni Universitá di Palermo Via Archirafi 34, 90123 Palermo, Italy. E-mail: {burderi,giusi,restivo}@math.unipa.it;Dipartimento di Matematica e Applicazioni Universitá di Palermo Via Archirafi 34, 90123 Palermo, Italy. E-mail: {burderi,giusi,restivo}@math.unipa.it;Dipartimento di Matematica e Applicazioni Universitá di Palermo Via Archirafi 34, 90123 Palermo, Italy. E-mail: {burderi,giusi,restivo}@math.unipa.it
Venue:
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
Year:
2006

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Abstract

In this paper we investigate properties of different classes of discrete sets with respect to the partial-order of subpicture. In particular we take in consideration the classes of convex polyominoes and L-convex polyominoes. In the first part of the paper we study closure properties of these classes with respect the order and we give a new characterization of L-convex polyominoes. In the second part we pose the question to extend Higman's theoremto discrete sets. We give a negative answer in the general case and we prove that the set of L-convex polyominoes is well-partially-ordered by using a representation of L-convex polyominoes in terms of words of a regular language.