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

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.

v4: 25 pages, 5 figures; this version focusses on order-theoretic aspects of our move-minimizing puzzles; other manuscripts make connections to combinatorial representation theory