Move-minimizing puzzles and diamond-colored modular/distributive lattices
Combinatorics
2023-12-05 v4
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.
Keywords
Cite
@article{arxiv.1710.01597,
title = {Move-minimizing puzzles and diamond-colored modular/distributive lattices},
author = {Robert G. Donnelly and Elizabeth A. Donovan and Molly W. Dunkum and Timothy A. Schroeder},
journal= {arXiv preprint arXiv:1710.01597},
year = {2023}
}
Comments
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