Math @ Duke

Publications [#243903] of Ezra Miller
Papers Published
 with Guo, A; Miller, E, Algorithms for Lattice Games,
International Journal of Game Theory, vol. 42 no. 4
(2013),
pp. 777788, ISSN 00207276 [math.CO/1105.5413], [DOI:10.1007/s0018201203199], [doi]
(last updated on 2017/12/14)
Abstract: This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games (Guo et al. Oberwolfach Rep 22: 2326, 2009; Guo and Miller, Adv Appl Math 46:363378, 2010). Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a given position is a winning position, and to find a move to a winning position, if not; and (ii) to decide whether two given positions are congruent, in the sense of misère quotient theory (Plambeck, Integers, 5:36, 2005; Plambeck and Siegel, J Combin Theory Ser A, 115: 593622, 2008). The methods are based on the theory of short rational generating functions (Barvinok and Woods, J Am Math Soc, 16: 957979, 2003). © 2012 SpringerVerlag.


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