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LIM is not slim

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Abstract

In this paper LIM, a recently proposed impartial combinatorial ruleset, is analyzed. A formula to describe the \(\mathcal G \)-values of LIM positions is given, by way of analyzing an equivalent combinatorial ruleset LIM’, closely related to the classical nim. Also, an enumeration of \(\mathcal P \)-positions of LIM with \(n\) stones, and its relation to the Ulam-Warburton cellular automaton, is presented.

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Notes

  1. Etymological note: the name LIM, aside from rhyming with nim, is an acronym for Laura e Manuel, the names of Silva’s children (the Portuguese word e “and” is pronounced / i /).

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Acknowledgments

The study reported here was largely carried out at the 2012 Games at Dal meeting, which we thank Richard Nowakowski for organizing. We also thank David Wolfe for useful discussions.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Alex Fink

  2. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot,  76100, Israel

    Aviezri S. Fraenkel

  3. High Institute of Education and Science, CIMA-UE, Lisbon, Portugal

    Carlos Santos

Authors
  1. Alex Fink
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  2. Aviezri S. Fraenkel
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  3. Carlos Santos
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Correspondence to Carlos Santos.

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Fink, A., Fraenkel, A.S. & Santos, C. LIM is not slim. Int J Game Theory 43, 269–281 (2014). https://doi.org/10.1007/s00182-013-0380-z

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  • DOI: https://doi.org/10.1007/s00182-013-0380-z

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