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The RSK correspondence generalises the Robinson-Schensted correspondence by replacing permutation matrices by matrices with entries in N, and standard Young tableaux by semistandard ones. For r ∈ N >0 , the Robinson-Schensted correspondence can be trivially extended, using the r-quotient map, to one between r-coloured permutations and pairs of standard… (More)

We elaborate on the results in [CaLe]. We give bijective proofs of a number of identities that were established there, in particular between the Yamanouchi domino tableaux and the Littlewood-Richardson tableaux that correspond to the same tensor product decomposition. The oldest form of the Robinson-Schensted correspondence, given in [Rob], associates to… (More)

An overview is provided of some of the basic facts concerning rim hook lattices and ribbon tableaux, using a representation of partitions by their edge sequences. An action is defined of the affine Coxeter group of type˜A r−1 on the r-rim hook lattice, and thereby on the sets of standard and semistandard r-ribbon tableaux, and this action is related to the… (More)

The following text is an annotation to Marc A. A. van Leeuwen's paper " Tableau algorithms defined naturally for pictures " in its version of 25 November 2011. This annotation contains corrections of a few mistakes. Different comments are separated by horizontal lines, like this: Page 1, §1: Replace " as a tableaux " by " as tableaux ". Page 3, §2.2:… (More)

We give a bijective proof of the Aztec diamond theorem, stating that there are 2 n(n+1)/2 domino tilings of the Aztec diamond of order n. The proof in fact establishes a similar result for non-intersecting families of n + 1 Schröder paths, with horizontal, diagonal or vertical steps, linking the grid points of two adjacent sides of an n × n square grid;… (More)

We introduce a set of operations that we call crystal operations on matrices with entries either in {0, 1} or in N. There are horizontal and vertical forms of these operations, which commute with each other, and they give rise to two different structures of a crystal graph of type A on these sets of matrices. They provide a new perspective on many aspects… (More)

We discuss several well known results about Schur functions that can be proved using cancellations in alternating summations; notably we shall discuss the Pieri and Murnaghan-Nakayama rules, the Jacobi-Trudi identity and its dual (Von Nägelsbach-Kostka) identity, their proofs using the correspondence with lattice paths of Gessel and Viennot, and finally the… (More)

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