Puzzles, Tableaux and Mosaics

Understand

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.