## Puzzles, tableaux, and mosaics

##### J. Algebr. Comb. 28(4), 461-480 (2008)
DOI: 10.1007/s10801-007-0110-3

### Summary

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/Phrases

keywords Littlewood-Richardson rule, puzzles, jeu de taquin