We consider a conditioned Galton–Watson tree and prove an estimate of the number of pairs of vertices with a given distance, or, equivalently, the number of paths of a given leng...
In a previous work [26], by considering paths that are partially weighted, the generating function of Dyck paths was shown to possess a type of symmetry, called an exchange relati...
Let fr n(k) be the number of 132-avoiding permutations on n letters that contain exactly r occurrences of 12 . . . k, and let Fr(x; k) and F (x, y; k) be the generating functions d...
We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to...
Let An denote the number of objects of some type of "size" n, and let Cn denote the number of these objects which are connected. It is often the case that there is a rel...
Several authors have examined connections between restricted permutations and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for color...
We compute the generating function for triangulations on a cylinder, with the restriction that all vertices belong to its boundary and that the intersection of a pair of different ...
Exponential stability of switched linear systems under both arbitrary and proper switching is studied through two suitably defined families of functions called the strong and the...