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

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## 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

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

## Related papers

## Cite this paper

APAChristos, J., Ollerton, R. & Shannon, A. (2008). Some combinatorial and recurrence relations for shapes in a trellis. Notes on Number Theory and Discrete Mathematics, 14(2), 1-10.

ChicagoChristos, JTA, and AG Shannon. “Some Combinatorial and Recurrence Relations for Shapes in a Trellis.” Notes on Number Theory and Discrete Mathematics 14, no. 2 (2008): 1-10.

MLAChristos, JTA, and AG Shannon. “Some Combinatorial and Recurrence Relations for Shapes in a Trellis.” Notes on Number Theory and Discrete Mathematics 14.2 (2008): 1-10. Print.