Geodesic
Diagonal checker-jumping and Eulerian numbers for color-signed permutations
The electronic journal of combinatorics, Tome 7 (2000)
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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.
DOI : 10.37236/1481
Classification : 05A30, 91A99, 11B37, 11B68
Mots-clés : Eulerian numbers, colour-signed permutations, checker-jumping game 
@article{10_37236_1481,
     author = {Niklas Eriksen and Henrik Eriksson and Kimmo Eriksson},
     title = {Diagonal checker-jumping and {Eulerian} numbers for color-signed permutations},
     journal = {The electronic journal of combinatorics},
     year = {2000},
     volume = {7},
     doi = {10.37236/1481},
     zbl = {0939.05014},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1481/}
}
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Niklas Eriksen; Henrik Eriksson; Kimmo Eriksson. Diagonal checker-jumping and Eulerian numbers for color-signed permutations. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1481

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