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Enumeration of generalized polyominoes

URN to cite this document: urn:nbn:de:bvb:703-opus-4126

Title data

Koch, Matthias ; Kurz, Sascha:
Enumeration of generalized polyominoes.
Bayreuth , 2006

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Abstract

Wir verallgemeinern den Begriff von Polyominoes (Tetrisbausteine) und betrachten Seite-an-Seite benachbarte überschneidungsfreie Vereinigungen von regelmäßigen k-Ecken. Für n<=4 geben wir Formeln für die Anzahl a_k(n) von verallgemeinerten Polyominoes, bestehend aus n regelmäßigen k-Ecken, an. Für weitere kleine Werte von k und n tabellieren wir durch computerunterstützte Enumeration gewonnene Anzahlen. Zum Abschluss erwähnen wir ein paar ungelöste Probleme für verallgemeinerte Polyominoes.

Abstract in another language

As a generalization of polyominoes we consider edge-to-edge connected nonoverlapping unions of regular k-gons. For n<=4 we determine formulas for the number a_k(n) of generalized polyominoes consisting of n regular k-gons. Additionally we give a table of the numbers a_k(n) for small k and n obtained by computer enumeration. We finish with some open problems for k-polyominoes.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): msc: 05B50; Source: Eingereicht an "The electronic journal of combinatorics"
Keywords: Kombinatorik; Polyominoes; Zellwachstumsproblem; erschöpfende Suche; Tetrisbausteine; Polyominoes; cell-growth problem; computer aided exact enumeration
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: German
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-opus-4126
Date Deposited: 25 Apr 2014 12:34
Last Modified: 27 Mar 2019 13:00
URI: https://epub.uni-bayreuth.de/id/eprint/740

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