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
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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