Noncommutative unicellular LLT polynomials

Jean-Christophe Novelli (1) , Jean-Yves Thibon (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

It is known that unicellular LLT polynomials are related to the quasi-symmetric chromatic polynomials of certain graphs by the (t-1)-transform of symmetric functions. We investigate the extension of this transformation to various combinatorial Hopf algebras and prove a noncommutative version of this property.

Domaines: Mathématiques [math]

Jean-Christophe Novelli, Jean-Yves Thibon. Noncommutative unicellular LLT polynomials. Journal of Combinatorial Theory, Series A, 2021, 177, pp.105305. ⟨10.1016/j.jcta.2020.105305⟩. ⟨hal-03492186⟩