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Enumeration of Planar Constellations
The enumeration of transitive ordered factorizations of a given permutation is a combinatorial problem related to singularity theory. Let n?1, and let ?0 be a permutation of Sn having di cycles of
Generating functions for generating trees
The relationship between structural properties of the rules defining such trees and the rationality, algebraicity, or transcendence of the corresponding generating functions are investigated.
A method for the enumeration of various classes of column-convex polygons
A new method is presented that allows to enumerate many classes of column-convex polygons, according to their perimeter, width and area, and defines implicitly the generating function for the class of polygons under consideration.
(2+2)-free Posets, Ascent Sequences and Pattern Avoiding Permutations
The ascent sequences that correspond to permutations avoiding the barred pattern $3\bar{1}52\ bar{4}$, and enumerate those permutations, thus settling a conjecture of Pudwell.
On the independence complex of square grids
Abstract The enumeration of independent sets of regular graphs is of interest in statistical mechanics, as it corresponds to the solution of hard-particle models. In 2004, it was conjectured by
Lattice animals and heaps of dimers
Two natural classes of heaps that are supersets of pyramids and are in bijection with certain classes ofanimals are found and enumerate them exactly, resulting in new classes ofsquare lattice animals that are both large and exactly enumerable.
Families of prudent self-avoiding walks
This work designs an isotropic family of prudent walks on the triangular lattice, which the generating function is proved to be non-finite and the end-to-end distance of these walks is studied and random generation procedures are provided.
Polynomial equations with one catalytic variable, algebraic series and map enumeration
It is proved that, under a mild hypothesis on the form of this equation, these k + 1 series are algebraic, and a strategy to compute a polynomial equation for each of them is given, which generalizes the so-called kernel method and quadratic method.
Counting Walks in the Quarter Plane
We study planar walks that start from a given point (i0j0), take their steps in a finite set \(\mathfrak{S}\), and are confined in the first quadrant x ≥ 0, y ≥ 0. Their enumeration can be attacked
The site-perimeter of bargraphs
This work enumerates (by their site-perimeter) the simplest family of polyominoes that are not fully convex-bargraphs, a type that has never been encountered so far in the combinatorics literature: a q-series into which an algebraic series has been substituted.