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The Pieri Rule for Dual Immaculate Quasi-Symmetric Functions

Annals of Combinatorics volume 20, pages 283–300 (2016)Cite this article

Abstract

The immaculate basis of the non-commutative symmetric functions was recently introduced by the first and third authors to lift certain structures in the symmetric functions to the dual Hopf algebras of the non-commutative and quasi-symmetric functions. It was shown that immaculate basis satisfies a positive, multiplicity free right Pieri rule. It was conjectured that the left Pieri rule may contain signs but that it would be multiplicity free. Similarly, it was also conjectured that the dual quasi-symmetric basis would also satisfy a signed multiplicity free Pieri rule. We prove these two conjectures here.

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Authors and Affiliations

  1. Fields Institute for Research in Mathematical Sciences, 222 College Street, Second Floor, Toronto, Ontario, M5T 3J1, Canada

    Nantel Bergeron, Juana Sánchez-Ortega & Mike Zabrocki

  2. Department of Mathematics and Statistics, York University, North York, Ontario, M3J 1P3, Canada

    Nantel Bergeron, Juana Sánchez-Ortega & Mike Zabrocki

  3. Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, M5S 2E4, Canada

    Juana Sánchez-Ortega

  4. Department of Algebra, Geometry and Topology, Universidad de Málaga, 29071, Málaga, Spain

    Juana Sánchez-Ortega

Authors
  1. Nantel Bergeron
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  2. Juana Sánchez-Ortega
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  3. Mike Zabrocki
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Correspondence to Nantel Bergeron.

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Bergeron, N., Sánchez-Ortega, J. & Zabrocki, M. The Pieri Rule for Dual Immaculate Quasi-Symmetric Functions. Ann. Comb. 20, 283–300 (2016). https://doi.org/10.1007/s00026-016-0303-3

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  • DOI: https://doi.org/10.1007/s00026-016-0303-3

Mathematics Subject Classification

  • 05E05

Keywords

  • non-commutative symmetric functions
  • quasi-symmetric functions
  • tableaux
  • Schur functions