2013/07/31 by Nantel Bergeron, Juana Sánchez-Ortega, Mike Zabrocki · 10 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Basis (linear algebra) #Dual (grammatical number) #Lift (data mining) #Multiplicity (mathematics) #Symmetric function #math.CO
paper · pdf · doi:10.1007/s00026-016-0303-3
published in Annals of Combinatorics 20(2), 283-300 (Birkhäuser) · 14 pages, corrections from v1 and v2
arxiv created 2014/07/30 · openalex publication_date 2016/01/21 · openalex created_date 2016/06/24 · arxiv updated 2016/11/08 · openalex updated_date 2026/08/05
The immaculate basis of the non-commutative symmetric functions was recently introduced by the first and third author 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.