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Phys. Rev. E 48, R2339–R2342 (1993)

Staircase polygons and recurrent lattice walks

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M. L. Glasser
Department of Physics and Clarkson Institute for Statistical Physics, Clarkson University, Potsdam, New York 13699-5820

E. Montaldi
Dipartimento di Fisica, Università di Milano, Via Celoria 16, 20133 Milano, Italy

Received 22 July 1993; published in the issue dated October 1993

In this paper we derive a direct relationship between the staircase-polygon-generating function Zd of Guttmann and Prellberg [Phys. Rev. E 47, R2233 (1993)] and the generating function for recurrent lattice walks Pd for the simple (hyper-) cubic lattice in all dimensions d. A recursion formula is obtained for the Zd with respect to dimension, which leads to a simplified derivation of Guttmann and Prellberg’s result for d=3, avoiding the use of the Heun function, and a derivation of their formula for d=4 from an integral representation is given in the Appendix.

© 1993 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.48.R2339
DOI:
10.1103/PhysRevE.48.R2339
PACS:
64.60.Ak, 36.20.Ey, 75.40.Cx
 
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