Vertaisarvioitu artikkeli konferenssijulkaisussa (A4)

On Perfect Coverings of Two-Dimensional Grids

Julkaisun tekijät: Heikkilä Elias, Herva Pyry, Kari Jarkko

Konferenssin vakiintunut nimi: International Conference on Developments in Language Theory

Paikka: Cham

Julkaisuvuosi: 2022

Journal: Lecture Notes in Computer Science

Kirjan nimi *: Developments in Language Theory: 26th International Conference, DLT 2022, Tampa, FL, USA, May 9–13, 2022, Proceedings

Sarjan nimi: Lecture Notes in Computer Science

Volyymi: 13257

ISBN: 978-3-031-05577-5

eISBN: 978-3-031-05578-2

ISSN: 0302-9743

eISSN: 1611-3349




We study perfect multiple coverings in translation invariant graphs with vertex set Z2 using an algebraic approach. In this approach we consider any such covering as a two-dimensional binary configuration which we then express as a two-variate formal power series. Using known results, we conclude that any perfect multiple covering has a non-trivial periodizer, that is, there exists a non-zero polynomial whose formal product with the power series presenting the covering is a two-periodic configuration. If a non-trivial periodizer has line polynomial factors in at most one direction, then the configuration is known to be periodic. Using this result we find many setups where perfect multiple coverings of infinite grids are necessarily periodic. We also consider some algorithmic questions on finding perfect multiple coverings.

Last updated on 2023-21-02 at 10:51