Geodesic
Puzzles, tableaux, and mosaics
Journal of Algebraic Combinatorics, Tome 28 (2008) no. 4, pp. 461-480.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is that we obtain bijective proofs of commutativity and associativity for the ring structures defined either of these objects. In particular, we obtain a new, easy proof of the Littlewood-Richardson rule. Finally we discuss how our operation is related to other known constructions, particularly jeu de taquin.
Keywords: keywords Littlewood-Richardson rule, puzzles, jeu de taquin 
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Purbhoo, Kevin. Puzzles, tableaux, and mosaics. Journal of Algebraic Combinatorics, Tome 28 (2008) no. 4, pp. 461-480. http://geodesic.mathdoc.fr/item/JAC_2008__28_4_a4/