• Citer

$e$-Positivity of vertical strip LLT polynomials

par D'Adderio, Michele
Référence Journal of combinatorial theory. Series A, 172, page (105212)
Publication Publié, 2020-01-01

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

In this article we prove the e-positivity of Gν[X;q+1] when Gν[X;q] is a vertical strip LLT polynomial. This property has been conjectured in [2] and [7], and it implies several e-positivities conjectured in those references and in [3]. We make use of a result of Carlsson and Mellit [5] that shows that a vertical strip LLT polynomial can be obtained by applying certain compositions of operators of the Dyck path algebra to the constant 1. Our proof gives in fact an algorithm to expand these symmetric functions in the elementary basis, and it shows, as a byproduct, that these compositions of operators are actually multiplication operators.