Schubert polynomials and $k$-Schur functions (Extended abstract)
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Abstract
The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function can be understood from the multiplication in the space of dual $k$-Schur functions. Using earlier work by the second author, we encode both problems by means of quasisymmetric functions. On the Schubert vs. Schur side, we study the $r$-Bruhat order given by Bergeron-Sottile, along with certain operators associated to this order. On the other side, we connect this poset with a graph on dual $k$-Schur functions given by studying the affine grassmannian order of Lam-Lapointe-Morse-Shimozono. Also, we define operators associated to the graph on dual $k$-Schur functions which are analogous to the ones given for the Schubert vs. Schur problem. Le but principal de cet article est de montrer que la multiplication d’un polynôme de Schubert de type fini $A$ par une fonction de Schur peut être comprise à partir de la multiplication dans l’espace dual des fonctions $k$-Schur. Les travaux antérieurs par le second auteur, nous permet de coder ces deux problèmes au moyen de fonctions quasi-symétriques. Du côté Schubert vs Schur, nous étudions l’ordre partiel $r$-Bruhat donné par Bergeron-Sottile, ainsi que certains opérateurs associés à cet ordre. Nous donnons une relation entre l’ordre $r$-Bruhat et le graphe de Bruhat sur les fonctions $k$-Schur duales données par l’étude de l’ordre affine grassmannienne de Lam-Lapointe-Morse-Shimozono. En outre, nous définissons des opérateurs associés a ce graphe qui sont analogues à ceux donnés pour le problème Schubert vs Schur.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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