Some combinatorial and recurrence relations for shapes in a trellis

J. T. A. Christos, R. L. Ollerton and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 14, 2008, Number 2, Pages 1–10
Full paper (PDF, 185 Kb)

Details

Authors and affiliations

J. T. A. Christos
PO Box 495, Balgowlah, NSW, 2093, Australia

R. L. Ollerton
University of Western Sydney
Kingswood DC 1797, Australia

A. G. Shannon
Warrane College, University of New South Wales
Kensington, NSW, 1465, Australia

Abstract

This paper considers the following problems from graph theory: in any section of given size of a trellis or wire-mesh fence, how many squares are there? how many rectangles are there? how many symmetric crosses are there? how many crosses in general? Certain patterns of arrays of numbers related to various substructures in terms of the numbers of edges and vertices in each case are listed and counted.

AMS Classification

• 05B35
• 51E30

References

1. Paul R Halmos. Want to be a Mathematician. New York: Springer-Verlag, 1985.
2. Kenneth E. Iverson. “Notation as a Tool of Thought.” Communications of the Association of Computing Machinery 23.8 (1980): 444-465.
3. A.G. Shannon, “Fibonacci and Lucas Numbers and the Complexity of a Graph”, The Fibonacci Quarterly 16.1 (1978): 1-4.