Annals of Combinatorics 3 (1999) 451-473

Adsorbing Staircase Walks and Staircase Polygons

Buks van Rensburg

Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada

Received November 3, 1998

AMS Subject Classification: 05A15, 82B20, 82B23, 82B41

Abstract. The adsorption of staircase walks and staircase polygons on the main diagonal in the square lattice is reviewed. We draw attention to the connection between adsorbing random walks in subsets of the integers and the square lattice, and this problem. The generating functions of adsorbing staircase walks and polygons are determined using several techniques, and information about the adsorption transition is found by the calculation of a critical exponent associated with it.

Keywords: staircase walks, dyck paths, adsorption, staircase polygons


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