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Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice
Dominique Gouyou-Beauchamps, Pierre Leroux
Hexagonal polyominoes are polyominoes on the honeycomb lattice. We enumerate the symmetry classes of convex hexagonal polyominoes. Here convexity is to be understood as convexity a…
Enumerative problems inspired by Mayer's theory of cluster integrals
Pierre Leroux
The basic functional equations for connected and 2-connnected graphs can be traced back to the statistical physicists Mayer and Husimi. They play an essential role in establishing…
Labelled and unlabelled enumeration of -gonal 2-trees
G. Labelle, C. Lamathe, P. Leroux
In this paper, we generalize 2-trees by replacing triangles by quadrilaterals, pentagons or -sided polygons (-gons), where is fixed. This generalization, to -gon…
A classification of plane and planar 2-trees
G. Labelle, C. Lamathe, P. Leroux
We present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed species. We then deduce the…
Enumeration of Symmetry Classes of Parallelogram Polyominoes
Pierre Leroux, Etienne Rassart
Parallelogram polyominoes are a subclass of convex polyominoes in the square lattice that has been studied extensively in the literature. Recently congruence classes of convex poly…
Enumeration of m-ary cacti
Miklos Bona, Michel Bousquet, Gilbert Labelle +1
The purpose of this paper is to enumerate various classes of cyclically colored m-gonal plane cacti, called m-ary cacti. This combinatorial problem is motivated by the topological…