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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
19
votes
A chess question of W.T. Tutte
In the German chess problem magazine feenschach, Heft 214 Band XXIV, July-August 2015 pp 178-180, I pose & solve the following mathematical puzzle: "Consider the 25 chess positions deriving from the 2 …
4
votes
Can every involution of a symmetric directed graph be written as a power of another symmetry?
This answer builds upon Sam Hopkins' suggestion of an oriented toroidal grid, but it's more than a comment. Bottom line: need the grid to be $2^s$ by $2^s$ where $s\ge2$ to get the requested involutio …