Séminaire Lotharingien de Combinatoire, B52d (2005), 39 pp.

Piotr Pragacz

Architectonique des formules préférées d'Alain Lascoux

Abstract. This article, written in December 2004, is an expanded version of the author's lecture opening the LascouxFest at the Séminaire Lotharingien de Combinatoire in Domaine Saint-Jacques, Ottrott, March 29-31, 2004. We discuss here some aspects of the work of Alain Lascoux (and some of his coworkers), related to symmetric functions and, more generally, Schubert polynomials. We illustrate some of the techniques he uses: determinants, transformations of alphabets, reproducing kernels, planar displays, divided differences, and vertex operators. The aim of this article is to show to the reader working in Algebraic Combinatorics (and others!) what we can learn from Alain to make our computations more efficient and more exciting.

Received: December 29, 2004. Accepted: January 12, 2005. Final Version: January 16, 2005.

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