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Chess tableaux
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
2005 (English)In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 11, no 2, A3- p.Article in journal (Refereed) Published
Abstract [en]

A chess tableau is a standard Young tableau in which, for all i and j, the parity of the entry in cell ( i; j) equals the parity of i + j + 1. Chess tableaux were first defined by Jonas Sjostrand in his study of the sign-imbalance of certain posets, and were independently rediscovered by the authors less than a year later in the completely different context of composing chess problems with interesting enumerative properties. We prove that the number of 3 x n chess tableaux equals the number of Baxter permutations of n - 1, as a corollary of a more general correspondence between certain three-rowed chess tableaux and certain three-rowed Dulucq-Guibert nonconsecutive tableaux. The correspondence itself is proved by means of an explicit bijection. We also outline how lattice paths, or rat races, can be used to obtain generating functions for chess tableaux. We conclude by explaining the connection to chess problems, and raising some unanswered questions, e. g., there are striking numerical coincidences between chess tableaux and the Charney-Davis statistic; is there a combinatorial explanation?

Place, publisher, year, edition, pages
2005. Vol. 11, no 2, A3- p.
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-37822ISI: 000229759200001ScopusID: 2-s2.0-33750315153OAI: diva2:435296
QC 20110818Available from: 2011-08-18 Created: 2011-08-17 Last updated: 2011-08-18Bibliographically approved

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