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Spiralling in Plane Random Walk

Published online by Cambridge University Press:  20 November 2018

E. M. Wright
E. M. Wright*
Affiliation:
University of Aberdeen, Scotland
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A particle is initially at the origin in the (X, Y) plane and each successive step it takes is of unit length and parallel either to the X-axis or to the Y-axis. Its path of n steps is called a spiral if (i) the particle never occupies the same position twice, (ii) any turns the path makes are all counter-clockwise or all clockwise and (iii) for every m > n, the path can be continued to m steps without violating (i) or (ii).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 1 , February 1965 , pp. 1 - 6
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Hardy, G. H. and Wright, E. M., Theory of Numbers, 4th edition, Oxford (1960).Google Scholar
2. Melzak, Z. A., Partition Functions and Spiralling in Plane Random Walk, Can. Math. Bull. 6(1963), 231-237.Google Scholar
3. Wright, E. M., An enumerative proof of an identity of Jacobi, Journ. London Math. Soc. 40(1965), 55-57.Google Scholar