36 citations · 48 across the 2 of their papers we have counts for
4 papers
Exactly solved models of polyominoes and polygons
Mireille Bousquet-Mélou, Richard Brak
This chapter deals with the exact enumeration of certain classes of self-avoiding polygons and polyominoes on the square lattice. We present three general approaches that apply to…
Discrete excursions
Mireille Bousquet-Mélou
It is well-known that the length generating function E(t) of Dyck paths (excursions with steps +1 and -1) satisfies 1-E+t^2E^2=0. The generating function E^(k)(t) of Dyck paths of…
Three osculating walkers
Mireille Bousquet-Mélou
We consider three directed walkers on the square lattice, which move simultaneously at each tick of a clock and never cross. Their trajectories form a non-crossing configuration of…
Walks in the quarter plane: Kreweras' algebraic model
Mireille Bousquet-Mélou
We consider planar lattice walks that start from (0,0), remain inthe first quadrant i, j >= 0, and are made of three types of steps: North-East, West and South. These walks are kno…