Annals of Combinatorics

, Volume 20, Issue 2, pp 283–300 | Cite as

The Pieri Rule for Dual Immaculate Quasi-Symmetric Functions

  • Nantel Bergeron
  • Juana Sánchez-Ortega
  • Mike Zabrocki
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.

Keywords

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

Mathematics Subject Classification

05E05 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Nantel Bergeron
    • 1
    • 2
  • Juana Sánchez-Ortega
    • 1
    • 2
    • 3
    • 4
  • Mike Zabrocki
    • 1
    • 2
  1. 1.Fields Institute for Research in Mathematical SciencesTorontoCanada
  2. 2.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada
  3. 3.Department of MathematicsUniversity of TorontoTorontoCanada
  4. 4.Department of Algebra, Geometry and TopologyUniversidad de MálagaMálagaSpain

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