Algebraic properties for some permutation statistics

Vincent Vong (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

In this article, we study some quotient sets on permutations built from peaks, valleys, double rises and double descents. One part is dedicated to the enumeration of the cosets using the bijection of Francon-Viennot which is a bijection between permutations and the so-called Laguerre histories. Then we study the algebraic properties of these quotient sets. After having shown that some of them give rise to quotient algebras of $\mathbf{FQSym}$, we prove that they are also free.

Mots clés: Laguerre histories; increasing binary trees; Free quasi-symmetric functions; quotient algebra

Domaines: Mathématique discrète [cs.DM]

Vincent Vong. Algebraic properties for some permutation statistics. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), Jun 2013, Paris, France. pp.843-854, ⟨10.46298/dmtcs.2345⟩. ⟨hal-00825478⟩