Crystallization of Domineering Snowflakes

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Abstract

© Springer International Publishing Switzerland 2015. In this paper we present a combinatorial game-theoretic analysis of special Domineering positions. In particular we investigate complex positions that are aggregates of simpler fragments, linked via bridging squares. We aim to extend two theorems that exploit the characteristic of an aggregate of two fragments having as game-theoretic value the sum of the values of the fragments. We investigate these theorems to deal with the case of multiple-connected networks with arbitrary number of fragments, possibly also including cycles. As an application, we introduce an interesting, special Domineering position with value ∗2. We dub this position the Snowflake. We then show how from this fragment larger chains of Snowflakes can be built with known values, including flat networks of Snowflakes (a kind of crystallization).
Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages100-112
Number of pages13
ISBN (Print)9783319279916
DOIs
Publication statusPublished - 2015

Publication series

SeriesLecture Notes in Computer Science
Volume9525

Cite this

Uiterwijk, J. W. H. M. (2015). Crystallization of Domineering Snowflakes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 100-112). Springer Verlag. Lecture Notes in Computer Science, Vol.. 9525 https://doi.org/10.1007/978-3-319-27992-3_10