Geodesic
Poset Structures on (m+2)-angulations and Polynomial Bases of the Quotient by Gm-Quasisymmetric Functions
Séminaire lotharingien de combinatoire, Tome 77 (2017-2018)

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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. 

@article{SLC_2017-2018_77_a1,
     author = {Jean-Christophe Aval and Fr\'ed\'eric Chapoton},
     title = {Poset {Structures} on (m+2)-angulations and {Polynomial} {Bases} of the {Quotient} by {Gm-Quasisymmetric} {Functions}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {77},
     year = {2017-2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017-2018_77_a1/}
}
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Jean-Christophe Aval; Frédéric Chapoton. Poset Structures on (m+2)-angulations and Polynomial Bases of the Quotient by Gm-Quasisymmetric Functions. Séminaire lotharingien de combinatoire, Tome 77 (2017-2018). http://geodesic.mathdoc.fr/item/SLC_2017-2018_77_a1/