Walks in the quarter plane: Kreweras’ algebraic model
نویسندگان
چکیده
منابع مشابه
Walks in the quarter plane: Kreweras’ algebraic model
We consider planar lattice walks that start from (0, 0), remain in the first quadrant i, j ≥ 0, and are made of three types of steps: North-East, West and South. These walks are known to have remarkable enumerative and probabilistic properties: – they are counted by nice numbers (Kreweras 1965), – the generating function of these numbers is algebraic (Gessel 1986), – the stationary distribution...
متن کاملWalks in the Quarter Plane: Analytic Approach and Applications
In this survey we present an analytic approach to solve problems concerning (deterministic or random) walks in the quarter plane. We illustrate the recent breakthroughs in that domain with two examples. The first one is about the combinatorics of walks confined to the quarter plane, and more precisely about the numbers of walks evolving in the quarter plane and having given length, starting and...
متن کاملTwo non-holonomic lattice walks in the quarter plane
We present two classes of random walks restricted to the quarter plane whose generating function is not holonomic. The non-holonomy is established using the iterated kernel method, a recent variant of the kernel method. This adds evidence to a recent conjecture on combinatorial properties of walks with holonomic generating functions. The method also yields an asymptotic expression for the numbe...
متن کاملWalks with small steps in the quarter plane
Let S ⊂ {−1, 0, 1}2 \ {(0, 0)}. We address the enumeration of plane lattice walks with steps in S, that start from (0, 0) and always remain in the first quadrant {(i, j) : i ≥ 0, j ≥ 0}. A priori, there are 28 problems of this type, but some are trivial. Some others are equivalent to a model of walks confined to a half-plane: such models can be solved systematically using the kernel method, whi...
متن کاملClassifying lattice walks restricted to the quarter plane
This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walks with respect to the classes algebraic, transcendental holonomic and non-holonomic. The principal results are a new algebraic class related to Kreweras’ walks; two new non-holonomic classes; and enumer...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2005
ISSN: 1050-5164
DOI: 10.1214/105051605000000052