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Walk on a grid

Published online by Cambridge University Press:  15 February 2024

Manija Shahali  and
H. A. Shahali
Manija Shahali
Affiliation:
16869 SW 65th Avenue, #318 Lake Oswego, OR 97035 USA e-mail: manija@addbits.com
H. A. Shahali
Affiliation:
15332 Antioch St. Pacific Palisades, CA 90272 USA e-mail: h_a_shahali@hotmail.com
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Extract

There are various combinatorial questions on rectangular arrays consisting of points, numbers, fields or, in general, of symbols such as chessboards, lattices, and graphs. Many such problems in enumerative combinatorics come from other branches of science and technology like physics, chemistry, computer sciences and engineering; for example the following two very challenging problems from chemistry:Problem 1: Dimer problem (Domino tiling)In chemistry, a large molecule composed repeatedly from monomers as a long chain is called a polymer and a dimer is composed of two monomers (where: mono = 1, di = 2, poly = many and mer = part).

Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 571 , March 2024 , pp. 111 - 117
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Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

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References

Temperley, H. N. V., Fisher, M. E., Dimer problem in statistical mechanics – an exact result, Philosophical Magazine, 6 (68) (1961) pp. 1061–1063.CrossRefGoogle Scholar
Kasteleyn, P. W., The statistics of dimers on a lattice, I: The number of dimer arrangements on a quadratic lattice, Physica, 27 (12) (1961) pp. 1209–1225.CrossRefGoogle Scholar
Flory, P., Principles of polymer chemistry, Cornell University Press, (1953) p. 672.Google Scholar
Madras, N., Slade, G., The self-avoiding walk, Birkhäuser (1996).CrossRefGoogle Scholar