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  1. Home > Articles & Issues >
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  3. Quasisymmetric Schur ...
Conference paper

Quasisymmetric Schur functions

James Haglund (1) (2), Sarah Mason ORCID (3), Kurt Luoto (4), Steph van Willigenburg (5) (6)
(1) University of Pennsylvania
(2) University of Pennsylvania [Philadelphia]
(3) Davidson College
(4) University of Washington [Seattle]
(5) University of British Columbia
(6) University of British Columbia [Canada]
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Imported on
May 10, 2017
Published on
December 31, 2007
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Proceedings
DOI
10.46298/dmtcs.3605
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https://about.hal.science/hal-authorisation-v1
The Combinatorics of Macdonald Polynomials and Related Objects
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Quasisymmetric Schur functions

James Haglund (1) (2), Sarah Mason ORCID (3), Kurt Luoto (4), Steph van Willigenburg (5) (6)
(1) University of Pennsylvania
(2) University of Pennsylvania [Philadelphia]
(3) Davidson College
(4) University of Washington [Seattle]
(5) University of British Columbia
(6) University of British Columbia [Canada]
Abstract
English
We introduce a new basis for the algebra of quasisymmetric functions that naturally partitions Schur functions, called quasisymmetric Schur functions. We describe their expansion in terms of fundamental quasisymmetric functions and determine when a quasisymmetric Schur function is equal to a fundamental quasisymmetric function. We conclude by describing a Pieri rule for quasisymmetric Schur functions that naturally generalizes the Pieri rule for Schur functions.
French
Nous étudions une nouvelle base des fonctions quasisymétriques, les fonctions de quasiSchur. Ces fonctions sont obtenues en spécialisant les fonctions de Macdonald dissymétrique. Nous décrivons les compositions que donne une simple fonction quasisymétriques. Nous décrivons aussi une règle par certaines fonctions de Schur.
Keywords
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • nonsymmetric Macdonald polynomials
  • Pieri rule
  • quasisymmetric functions
  • Schur functions
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