Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 275-294 |
| Seitenumfang | 20 |
| Fachzeitschrift | Annals of combinatorics |
| Jahrgang | 17 |
| Ausgabenummer | 2 |
| Frühes Online-Datum | 13 Jan. 2013 |
| Publikationsstatus | Veröffentlicht - Juni 2013 |
Abstract
In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F-multiplicity free. Combinatorially, this is equivalent to classifying all skew shapes whose standard Young tableaux have distinct descent sets. We then generalize our setting, and classify all F-multiplicity free quasisymmetric Schur functions with one or two terms in the expansion, or one or two parts in the indexing composition. This identifies composition shapes such that all standard composition tableaux of that shape have distinct descent sets. We conclude by providing such a classification for quasisymmetric Schur function families, giving a classification of Schur functions that are in some sense almost F-multiplicity free.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
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in: Annals of combinatorics, Jahrgang 17, Nr. 2, 06.2013, S. 275-294.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Multiplicity Free Schur, Skew Schur, and Quasisymmetric Schur Functions
AU - Bessenrodt, C.
AU - van Willigenburg, S.
N1 - Funding Information: ∗The authors’ collaboration was supported in part by the Alexander von Humboldt Foundation and the National Sciences and Engineering Research Council of Canada.
PY - 2013/6
Y1 - 2013/6
N2 - In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F-multiplicity free. Combinatorially, this is equivalent to classifying all skew shapes whose standard Young tableaux have distinct descent sets. We then generalize our setting, and classify all F-multiplicity free quasisymmetric Schur functions with one or two terms in the expansion, or one or two parts in the indexing composition. This identifies composition shapes such that all standard composition tableaux of that shape have distinct descent sets. We conclude by providing such a classification for quasisymmetric Schur function families, giving a classification of Schur functions that are in some sense almost F-multiplicity free.
AB - In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F-multiplicity free. Combinatorially, this is equivalent to classifying all skew shapes whose standard Young tableaux have distinct descent sets. We then generalize our setting, and classify all F-multiplicity free quasisymmetric Schur functions with one or two terms in the expansion, or one or two parts in the indexing composition. This identifies composition shapes such that all standard composition tableaux of that shape have distinct descent sets. We conclude by providing such a classification for quasisymmetric Schur function families, giving a classification of Schur functions that are in some sense almost F-multiplicity free.
KW - compositions
KW - multiplicity free
KW - quasisymmetric function
KW - Schur function
KW - skew Schur function
KW - tableaux
UR - http://www.scopus.com/inward/record.url?scp=84878176952&partnerID=8YFLogxK
U2 - 10.1007/s00026-013-0177-6
DO - 10.1007/s00026-013-0177-6
M3 - Article
AN - SCOPUS:84878176952
VL - 17
SP - 275
EP - 294
JO - Annals of combinatorics
JF - Annals of combinatorics
SN - 0218-0006
IS - 2
ER -