We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
SOME LARGE POLYOMINOES' PERIMETER: A STOCHASTIC ANALYSIS.
- Authors
LOUCHARD, GUY
- Abstract
In this paper, we analyze the stochastic properties of some large size (area) polyominoes' perimeter such that the directed column-convex polyomino, the columnconvex polyomino, the directed diagonally-convex polyomino, the staircase (or parallelogram) polyomino, the escalier polyomino, the wall (or bargraph) polyomino. All polyominoes considered here are made of contiguous, not-empty columns, without holes, such that each column must be adjacent to some cell of the previous column. We compute the asymptotic (for large size n) Gaussian distribution of the perimeter, including the corresponding Markov property of the chain of columns, and the convergence to classical Brownian motions of the perimeter seen as a trajectory according to the successive columns. All polyominoes of size n are considered as equiprobable.
- Subjects
POLYOMINOES; STOCHASTIC analysis; POLYNOMIALS; HALL polynomials; LINEAR equations
- Publication
Online Journal of Analytic Combinatorics, 2020, Issue 15, p1
- ISSN
1931-3365
- Publication type
Article