### Abstract

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.

Original language | Italian |
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Pages (from-to) | 435-446 |

Number of pages | 12 |

Journal | Fundamenta Informaticae |

Volume | 74(4) |

Publication status | Published - 2006 |

## Cite this

Burderi, F., Restivo, A., & Castiglione, G. (2006). Highmann's Theorem on Discrete Sets.

*Fundamenta Informaticae*,*74(4)*, 435-446.