The role of residue and quotient tables in the theory of k-Schur functions

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:136

Article

Konvalinka, Matjaz

关键词: k-Schur functions;    Residue tables;    Quotient tables;    k-bounded partitions;    Cores;    Strong covers;    Weak strips;    Murnaghan-Nakayama rule;    Littlewood-Richardson rule;   

DOI  :  10.1016/j.jcta.2015.06.003

来源: Elsevier

【 摘 要 】

Recently, residue and quotient tables were defined by Fishel and the author, and were used to describe strong covers in the lattice of k-bounded partitions. In this paper, we prove (and, in some cases, conjecture) that residue and quotient tables can be used to describe many other results in the theory of k-bounded partitions and k-Schur functions, including k-conjugates, weak horizontal and vertical strips, and the Murnaghan-Nakayama rule. Evidence is presented for the claim that one of the most important open questions in the theory of k-Schur functions, a general rule that would describe their product, can be also concisely stated in terms of residue tables. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free