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Crystallization of Domineering Snowflakes

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Advances in Computer Games (ACG 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9525))

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Abstract

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).

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Author information

Authors and Affiliations

  1. Department of Knowledge Engineering (DKE), Maastricht University, Maastricht, The Netherlands

    Jos W. H. M. Uiterwijk

Authors
  1. Jos W. H. M. Uiterwijk
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Correspondence to Jos W. H. M. Uiterwijk .

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Editors and Affiliations

  1. Leiden University , Leiden, The Netherlands

    Aske Plaat

  2. Leiden University , Leiden, The Netherlands

    Jaap van den Herik

  3. Leiden University , Leiden, The Netherlands

    Walter Kosters

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Uiterwijk, J.W.H.M. (2015). Crystallization of Domineering Snowflakes. In: Plaat, A., van den Herik, J., Kosters, W. (eds) Advances in Computer Games. ACG 2015. Lecture Notes in Computer Science(), vol 9525. Springer, Cham. https://doi.org/10.1007/978-3-319-27992-3_10

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  • DOI: https://doi.org/10.1007/978-3-319-27992-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27991-6

  • Online ISBN: 978-3-319-27992-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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