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pro vyhledávání: '"Siegel, Aaron N."'
Autor:
Siegel, Aaron N.
The universe $\mathcal{E}$ of dead-ending partizan games has emerged as an important structure in the study of mis\`ere play. Here we attempt a systematic investigation of the structure of $\mathcal{E}$ and its subuniverses. We begin by showing that
Externí odkaz:
http://arxiv.org/abs/2312.16259
Autor:
Siegel, Aaron N.
We consider the abstract structure of the monoid M of mis\`ere impartial game values. Several new results are presented, including a proof that the group of fractions of M is almost torsion-free; a method of calculating the number of distinct games b
Externí odkaz:
http://arxiv.org/abs/2012.08554
In this article, we study the structure, and in particular the Grundy values, of a family of games known as memgames.
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Comment: Feedback welcome!
Externí odkaz:
http://arxiv.org/abs/1912.10517
Autor:
Plambeck, Thane E., Siegel, Aaron N.
We provide supplementary appendices to the paper Misere quotients for impartial games. These include detailed solutions to many of the octal games discussed in the paper, and descriptions of the algorithms used to compute most of our solutions.
Externí odkaz:
http://arxiv.org/abs/0705.2404
Autor:
Siegel, Aaron N.
We show that partizan games admit canonical forms in mis\`ere play. The proof is a synthesis of the canonical form theorems for normal-play partizan games and mis\`ere-play impartial games. It is fully constructive, and algorithms readily emerge for
Externí odkaz:
http://arxiv.org/abs/math/0703565
Autor:
Siegel, Aaron N.
A \emph{bipartite monoid} is a commutative monoid $\Q$ together with an identified subset $\P \subset \Q$. In this paper we study a class of bipartite monoids, known as \emph{mis\`ere quotients}, that are naturally associated to impartial combinatori
Externí odkaz:
http://arxiv.org/abs/math/0703070
Autor:
Siegel, Aaron N.
These lecture notes are based on a short course on mis\`ere quotients offered at the Weizmann Institute of Science in Rehovot, Israel, in November 2006. They include an introduction to impartial games, starting from the beginning; the basic mis\`ere
Externí odkaz:
http://arxiv.org/abs/math/0612616
Autor:
Plambeck, Thane E., Siegel, Aaron N.
Publikováno v:
Journal of Combinatorial Theory, Series A (May 2008) pp 593-622
We announce misere-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misere quotients--commutative monoids that encode the additive structure of specific misere-play games. We also introduce se
Externí odkaz:
http://arxiv.org/abs/math/0609825
Publikováno v:
In Journal of Combinatorial Theory, Series A February 2015 130:42-63
