Poset structures on (m + 2)-angulations and polynomial bases of the   quotient by G^m -quasisymmetric functions
  For integers m, n $\ge$ 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. 
Jean-Christophe Aval (LaBRI), Fr\'ed\'eric Chapoton (IRMA)
math.CO