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, Volume 35, Issue 2, pp 275–281 | Cite as

Counterexamples to Conjectures About Subset Takeaway and Counting Linear Extensions of a Boolean Lattice

  • Andries E. Brouwer
  • J. Daniel Christensen
Article

Abstract

We develop an algorithm for efficiently computing recursively defined functions on posets. We illustrate this algorithm by disproving conjectures about the game Subset Takeaway (Chomp on a hypercube) and computing the number of linear extensions of the lattice of a 7-cube and related lattices.

Keywords

Combinatorial game Impartial game Grundy number Partially ordered set Total order 

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Western OntarioLondonCanada

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