Abstract
We establish several properties of an algorithm defined by Mason and Remmel (2010) which inserts a positive integer into a row-strict composition tableau. These properties lead to a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. Nous établissons plusieurs propriétés d'un algorithme défini par Mason et Remmel (2010), qui insère un entier positif dans un tableau dont la forme est une composition, avec ordre strict sur les lignes (row-strict). Ces propriétés conduisent à une règle de type Littlewood-Richardson pour étendre le produit d'une fonction de Schur quasi-symétrique "row-strict'' et d'une fonction de Schur symétrique en termes de fonctions de Schur quasi-symétriques "row-strict''.
Highlights
Quasisymmetric functions were defined by Gessel in [5] where he developed many of their properties, quasisymmetric functions had already appeared in earlier work of Stanley [14]
In [7], the authors define a new basis CSα for the algebra QSym of quasisymmetric functions, where α is a sequence of positive integers called a strong composition
{ A filling of a skew diagram β γ is an assignment of positive integers to the boxes that are in β and not in γ
Summary
A Littlewood-Richardson type rule for row-strict quasisymmetric Schur functions. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
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