TY - JOUR

T1 - Highmann's Theorem on Discrete Sets

AU - Restivo, Antonio

AU - Castiglione, Giuseppa

AU - Burderi, Fabio

PY - 2006

Y1 - 2006

N2 - In this paper we investigate properties of different classes of discrete sets with respect tothe partial-order of subpicture. In particular we take in consideration the classes of convex polyominoesand L-convex polyominoes. In the first part of the paper we study closure properties of theseclasses with respect the order and we give a new characterization of L-convex polyominoes. In thesecond part we pose the question to extend Higman’s theoremto discrete sets. We give a negative answerin the general case and we prove that the set of L-convex polyominoes is well-partially-orderedby using a representation of L-convex polyominoes in terms of words of a regular language.

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

KW - Discrete sets

KW - polyominoes and L-convex polyominoes; subpicture order and wellpartial-ordering.

KW - Discrete sets

KW - polyominoes and L-convex polyominoes; subpicture order and wellpartial-ordering.

UR - http://hdl.handle.net/10447/40019

M3 - Article

VL - 74(4)

SP - 435

EP - 446

JO - Fundamenta Informaticae

JF - Fundamenta Informaticae

SN - 0169-2968

ER -