Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:137

Article

Bessenrodt, Christine¹  Tewari, Vasu²  van Willigenburg, Stephanie² 

[1] Leibniz Univ Hannover, Inst Algebra Zahlentheorie & Diskrete Math, D-30167 Hannover, Germany

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

关键词: Composition;    Littlewood-Richardson rule;    Quasisymmetric function;    Schur function;    Skew Schur function;    Symmetric function;    Tableaux;   

DOI  :  10.1016/j.jcta.2015.08.005

来源: Elsevier

【 摘 要 】

The classical Littlewood-Richardson rule is a rule for computing coefficients in many areas, and comes in many guises. In this paper we prove two Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions that are analogous to the famed version of the classical Littlewood-Richardson rule involving Yamanouchi words. Furthermore, both our rules contain this classical Littlewood-Richardson rule as a special case. We then apply our rules to combinatorially classify symmetric skew quasisymmetric Schur functions. This answers affirmatively a conjecture of Bessenrodt, Luoto and van Willigenburg. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free