Hex and combinatorics

Combinatorics Enumerative Combinatorics 05

Analytic Combinatorics — Symbolic Combinatorics

This booklet develops in nearly 200 pages the basics of combinatorial enumeration through an approach that revolves around generating functions. The major objects of interest here are words, trees, graphs, and permutations, which surface recurrently in all areas of discrete mathematics. The text presents the core of the theory with chapters on unlabelled enumeration and ordinary generating func...

Solving Hex: Beyond Humans

For the first time, automated Hex solvers have surpassed humans in their ability to solve Hex positions: they can now solve many 9×9 Hex openings. We summarize the methods that attained this milestone, and examine the future of Hex solvers.

MOHEX Wins Hex Tournament

The 2011 Hex competition started on Sunday November 20 and finished on Monday November 21. Three programs competed: PANORAMEX by Fabien Teytaud, Tristan Cazenave, and Nicolas Jouandeau from France; WOLVE by Broderick Arneson, Ryan Hayward, and Philip Henderson from Canada; and MOHEX by Philip Henderson, Broderick Arneson, and Ryan Hayward. This year Aja Huang from Taiwan and Jakub Pawlewicz fro...

Solving 8x8 Hex

Using efficient methods that reduce the search space, we design an algorithm strong enough to solve all 8×8 Hex openings.