NDLI: Puzzles, tableaux, and mosaics

Content Provider	Springer Nature Link
Author	Purbhoo, Kevin
Copyright Year	2007
Abstract	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.
Starting Page	461
Ending Page	480
Page Count	20
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	28
Issue Number	4
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2007-12-05
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Littlewood-Richardson rule Puzzles Jeu de taquin Group Theory and Generalizations Computer Science Order, Lattices, Ordered Algebraic Structures Convex and Discrete Geometry Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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Puzzles, tableaux, and mosaics