© 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).
|Title of host publication||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Number of pages||13|
|Publication status||Published - 2015|
|Series||Lecture Notes in Computer Science|
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