Marc van Leeuwen

Links to other pages on this site

• LiE home page
• LiE online service
• CWEBx home page
• Small computer programs
• Enseignement

General information

And here is my Curriculum vitae with list of publications.

Atlas of Lie groups and Representations

In March 2007 this project has obtained sudden (and probably short-lived) celebrity after the publication of the successful completion, in January 2007, of the computation of the 453060×453060 matrix of Kazhdan-Lusztig-Vogan polynomials for the big block of the split real Lie group of type E₈. It should be noted that such matrices for all other cases of interest could already be computed by the atlas software as of December 2005. In that development I have played no role, but I have in the effort to squeeze the huge computation necessary for the final case into the limited amount of RAM (64GiB) that we had available for it (or more precisely the machine that William Stein had kindly given us the use of). Here are a local press release and a slides of a persentation (in French).

Publications

My thesis

Algebraic Combinatorics

• An Application of Hopf Algebra techniques to Representations of Finite Classical Groups, Journal of algebra Vol 140 (1991)
• The Robinson-Schensted and Schützenberger algorithms, an elementary approach Electronic Journal of Combinatorics, Foata Festschrift, Vol 3(no.2), R15 (1996)
• Tableau algorithms defined naturally for pictures Discrete Mathematics 157 (1996);
• Edge sequences, ribbon tableaux, and an action of affine permutations Europ. J. Combinatorics 20 (1999)
• Some bijective correspondences involving domino tableaux Electronic Journal of Combinatorics Vol 7(1) R35 (2000), and arXiv:math.CO/9909119.
• Flag varieties, and interpretations of Young tableau algorithms Journal of Algebra 224 (2000), and arXiv:math.CO/9908041
• An analogue of Jeu de taquin for Littelmann's crystal paths Séminaire Lotharingien de Combinatoire, B41b (1998)
• The Littlewood-Richardson rule, and related combinatorics in Math. Soc. of Japan Memoirs 11, Interaction of Combinatorics and Representation Theory; a slightly earlier version is available as arXiv:math.CO/9908099
• Spin-preserving Knuth correspondences for ribbon tableaux Electronic Journal of Combinatorics Vol 12(1) R10 (2005), an earlier version appeared as arXiv:math.CO/0312020).
• Schur functions and alternating sums Electronic Journal of Combinatorics Vol 11(2) A5 (2006), also available as arXiv:math.CO/0602357).
• Double crystals of binary and integral matrices Electronic Journal of Combinatorics Vol 13(1) R86 (2006), also available as arXiv:math.CO/0605420).
• Some simple bijections involving lattice walks and ballot sequences, also available as arXiv:1010.4847
• with Frédéric Bosio: A bijection proving the Aztec diamond theorem by combing lattice paths, Electronic Journal of Combinatorics Vol 20(4) P24, also available as hal-00734890 or arXiv:1209.5373.

Computer Algebra

• The LiE manual with A. M. Cohen and B. Lisser, part of the LiE computer algebra package
• LiE, A software package for Lie group computations (a 39 Kb dvi file) Euromath Bulletin 1, No 2 (1994)
• Termination for a class of algorithms for constructing algebras given by generators and relations (a 65 Kb dvi file) Journal of Pure and Applied Algebra 117&118 (1997);

Literate Programming

• The CWEBx manual (a 210 Kb dvi file) part of the CWEBx distribution;

You may also have a look at the preprints that I wrote at CWI (in Postscript format).

Software

Public packages

• CWEBx, an improved version of the CWEB system for Literate Programming in C, by Sylvio Levy and Donald E. Knuth
• LiE, a computer algebra package Lie group computations; a software project headed by Arjeh M. Cohen (it requires CWEBx)

Personal projects

Other interests