The algebraic solvability of the novel lamplighter puzzle

Autor:	Connor Gregor, Daniel Ashlock, Allan R. Willms
Rok vydání:	2022
Předmět:	Human-Computer Interaction Mathematics::Group Theory Mathematics::K-Theory and Homology Computational Mechanics Computer Science (miscellaneous) Mathematics::Metric Geometry Computer Graphics and Computer-Aided Design
Zdroj:	ICGA Journal. 43:203-225
ISSN:	2468-2438 1389-6911
DOI:	10.3233/icg-210195
Popis:	In this study, the group of finite cyclic lamplighter states is reinterpreted as the novel lamplighter puzzle. The rules of the puzzle are outlined and related back to properties of the lamplighter group with specific interest placed upon the discussion of which puzzle instances are solvable. The paper shows that, through the use of algebra, many puzzle instances can be identified as solvable without the use of an exhaustive search algorithm. Solvability depends upon the creation of irregular generating sets for subgroups of the finite cyclic lamplighter group and the cosets formed by these subgroups. Further possible generalizations of the lamplighter puzzle are also discussed in closing.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c56d79c0c1ef2c70ab53faacb887113f https://doi.org/10.3233/icg-210195 Zobrazit plný text záznamu