Move-minimizing puzzles and diamond-colored modular/distributive lattices

2017/10/02 by Donnelly, Robert G., Donovan, Elizabeth A., Dunkum, Molly W. +1
#06A07 (06C99 #06D99) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.01597

Abstract

The move-minimizing puzzles presented here are certain types of one-player combinatorial games that are shown to have explicit solutions whenever they can be encoded in a certain way as diamond-colored modular or distributive lattices. Our work here is founded in a new interpretation of some routine and elementary order-theoretic combinatorics.

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