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- Marc A. A. van Leeuwen
- Electr. J. Comb.
- 2005

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)

Littelmann has given a combinatorial model for the characters of representations of semisimple Lie algebras, in terms of certain paths traced in the space of (rational) weights. From it, a description of the decomposition of tensor products can be derived that generalises the Littlewood-Richardson rule (the latter is valid in type An only). We present a new… (More)

- Marc A. A. van Leeuwen
- Electr. J. Comb.
- 2000

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. 1991 Mathematics Subject Classification: 05E10.

Page 4, §1.3: You claim that ”this representation is not unique in general (although in some cases it is, for instance when the sets of rows and columns meeting D are both initial intervals of N)”. This is not literally correct, since the representation is not unique when D is the empty skew diagram, whereas it is clear that the sets of rows and columns… (More)

The conjugacy classes of nilpotent n × n matrices can be parametrised by partitions λ of n, and for a nilpotent η in the class parametrised by λ, the variety Fη of η-stable flags has its irreducible components parametrised by the standard Young tableaux of shape λ. We indicate how several algorithmic constructions defined for Young tableaux have… (More)

- Marc A. A. van Leeuwen
- Eur. J. Comb.
- 1999

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 Ãr−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)

- Marc A. A. van Leeuwen
- Discrete Mathematics
- 1996

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)

- Marc A. A. van Leeuwen
- Electr. J. Comb.
- 2006

Abstract 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 JacobiTrudi identity and its dual (Von Nägelsbach-Kostka) identity, their proofs using the correspondence with lattice paths of Gessel and Viennot, and… (More)

- Frédéric Bosio, Marc A. A. van Leeuwen
- Electr. J. Comb.
- 2013

We give a bijective proof of the Aztec diamond theorem, stating that there are 2n(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; these… (More)

- Marc A. A. van Leeuwen
- Electr. J. Comb.
- 2006

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)