Séminaire Lotharingien de Combinatoire, B77b (2016), 14 pp.

Jean-Christophe Aval and Frédéric Chapoton

Poset Structures on (m+2)-angulations and Polynomial Bases of the Quotient by Gm-Quasisymmetric Functions

Abstract. For integers m, n >= 1, we describe a bijection sending dissections of the (mn+2)-regular polygon into (m+2)-sided polygons to a new basis of the quotient of the polynomial algebra in mn variables by an ideal generated by some kind of higher quasi-symmetric functions. We show that divisibility of the basis elements corresponds to a new partial order on dissections, which is studied in some detail.

Received: August 30, 2016. Revised: November 24, 2016. Accepted: December 1, 2016.

The following versions are available: