Formulae for polyominoes on twisted cylinders

Gadi Aleksandrowicz, Andrei Asinowski, Gill Barequet, Ronnie Barequet

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Polyominoes are edge-connected sets of cells on the square lattice ℤ2. We investigate polyominoes on a square lattice embedded on so-called twisted cylinders of a bounded width (perimeter) w. We prove that the limit growth rate of polyominoes of the latter type approaches that of polyominoes of the former type, as w tends to infinity. We also prove that for any fixed value of w, the formula enumerating polyominoes on a twisted cylinder of width w satisfies a linear recurrence whose complexity grows exponentially with w. By building the finite automaton that "grows" polyominoes on the twisted cylinder, we obtain the prefix of the sequence enumerating these polyominoes. Then, we recover the recurrence formula by using the Berlekamp-Massey algorithm.

Original languageEnglish
Title of host publicationLanguage and Automata Theory and Applications - 8th International Conference, LATA 2014, Proceedings
Pages76-87
Number of pages12
DOIs
StatePublished - 2014
Event8th International Conference on Language and Automata Theory and Applications, LATA 2014 - Madrid, Spain
Duration: 10 Mar 201414 Mar 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8370 LNCS

Conference

Conference8th International Conference on Language and Automata Theory and Applications, LATA 2014
Country/TerritorySpain
CityMadrid
Period10/03/1414/03/14

Keywords

  • Recurrence formula
  • generating function
  • transfer matrix

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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