A method for the enumeration of various classes of column-convex polygons
Discrete Mathematics
Basic analytic combinatorics of directed lattice paths
Theoretical Computer Science
Polynomial equations with one catalytic variable, algebraic series and map enumeration
Journal of Combinatorial Theory Series B
Analytic Combinatorics
Matrices and Matroids for Systems Analysis
Matrices and Matroids for Systems Analysis
Area limit laws for symmetry classes of staircase polygons
Combinatorics, Probability and Computing
| Hi-index | 0.00 |
We study limit distributions for random variables defined in terms of coefficients of a power series which is determined by a certain linear functional equation. Our technique combines the method of moments with the kernel method of algebraic combinatorics. As limiting distributions the area distributions of the Brownian excursion and meander occur. As combinatorial applications we compute the area laws for discrete excursions and meanders with an arbitrary finite set of steps and the area distribution of column convex polygons. As a by-product of our approach we find the joint distribution of signed areas and final altitude of a Brownian motion in terms of joint moments.