LOU, a Maple package to study Lou Kauffman’s linguistic approach to the Four Color Theorem. It is one of the two packages accompanying the article ”Toward a language theoretic proof of the four color theorem”. This paper considers the problem of showing that every pair of binary trees with the same number of leaves parses a common word under a certain simple grammar. We enumerate the common parse words for several infinite families of tree pairs and discuss several ways to reduce the problem of finding a parse word for a pair of trees to that for a smaller pair. The statement that every pair of trees has a common parse word is equivalent to the statement that every planar graph is four-colorable, so the results are a step toward a language theoretic proof of the four color theorem.
Keywords for this software
References in zbMATH (referenced in 3 articles , 1 standard article )
Showing results 1 to 3 of 3.
- Csar, Sebastian A.; Sengupta, Rik; Suksompong, Warut: On a subposet of the Tamari lattice (2014)
- Cooper, Bobbe; Rowland, Eric; Zeilberger, Doron: Toward a language theoretic proof of the four color theorem (2012)
- Madonia, Maria; Scollo, Giuseppe: Reducibility and solvability of some classes of Kryuchkov binary tree pairs (2012)