Diagonal Checker-jumping and Eulerian Numbers for Color-signed Permutations

Niklas Eriksen, Henrik Eriksson, Kimmo Eriksson


We introduce color-signed permutations to obtain a very explicit combinatorial interpretation of the $q$-Eulerian identities of Brenti and some generalizations. In particular, we prove an identity involving the golden ratio, which allows us to compute upper bounds on how high a checker can reach in a classical checker-jumping problem, when the rules are relaxed to allow also diagonal jumps.

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