Result: Diagonal Checker-jumping and Eulerian Numbers for Color-signed Permutations: Diagonal checker-jumping and Eulerian numbers for color-signed permutations

Title:
Diagonal Checker-jumping and Eulerian Numbers for Color-signed Permutations: Diagonal checker-jumping and Eulerian numbers for color-signed permutations
Authors:
Eriksen, Niklas, Eriksson, Henrik, Eriksson, Kimmo
Source:
The Electronic Journal of Combinatorics. 7
Publisher Information:
The Electronic Journal of Combinatorics, 2000.
Publication Year:
2000
Subject Terms:
Matematik, \(q\)-calculus and related topics, Recurrences, checker-jumping game, 0102 computer and information sciences, colour-signed permutations, 0101 mathematics, Bernoulli and Euler numbers and polynomials, Eulerian numbers, 01 natural sciences, Mathematics, Game theory
Document Type:
Academic journal Article
File Description:
application/xml; application/pdf
ISSN:
1077-8926
DOI:
10.37236/1481
Access URL:
https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r3/pdf
https://zbmath.org/1409045
http://www.diva-portal.org/smash/record.jsf?pid=diva2:781052
http://univie.ac.at/emis/journals/ejc/volume_7/pdf/v7i1r3.pdf
https://dblp.uni-trier.de/db/journals/combinatorics/combinatorics7.html#EriksenEE00
https://www.combinatorics.org/Volume_7/Abstracts/v7i1r3.html
http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-41763
Accession Number:
edsair.doi.dedup.....0752d51cb2b0c4d619bf5d9e1f88b911
Database:
OpenAIRE

Further Information

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.