J. Haglund ; K. Luoto ; S. Mason ; S. van Willigenburg - Refinements of the Littlewood-Richardson rule

dmtcs:2744 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2744
Refinements of the Littlewood-Richardson ruleArticle

Authors: J. Haglund 1; K. Luoto 2; S. Mason 3; S. van Willigenburg 4

We refine the classical Littlewood-Richardson rule in several different settings. We begin with a combinatorial rule for the product of a Demazure atom and a Schur function. Building on this, we also describe the product of a quasisymmetric Schur function and a Schur function as a positive sum of quasisymmetric Schur functions. Finally, we provide a combinatorial formula for the product of a Demazure character and a Schur function as a positive sum of Demazure characters. This last rule implies the classical Littlewood-Richardson rule for the multiplication of two Schur functions.

https://doi.org/10.46298/dmtcs.2744
Source: HAL:hal-01185437v1
Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: key polynomials,nonsymmetric Macdonald polynomials,Littlewood-Richardson rule,quasisymmetric functions,Schur functions,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • The Combinatorics of Macdonald Polynomials and Related Objects; Funder: National Science Foundation; Code: 0901467
  • Funder: Natural Sciences and Engineering Research Council of Canada
  • The Combinatorics of Macdonald Polynomials; Funder: National Science Foundation; Code: 0553619
  • PostDoctoral Research Fellowship; Funder: National Science Foundation; Code: 0603351

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