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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 *G*^{m}-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.

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