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

Abstract. 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 checkerjumping problem, when the rules are relaxed to allow also diagonal jumps.

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Niklas Eriksen, Henrik Eriksson, Kimmo Eriksson
• Keywords: COMBINATORICS 2000, Explicit Combinatorial Interpretation, Golden Ratio, Q-Eulerian Identities