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Stop-sign theorems and binomial coefficients*

Published online by Cambridge University Press:  23 January 2015

Peter Hilton and
Jean Pedersen
Peter Hilton
Affiliation:
Mathematical Sciences Department, SUNY at Binghamton, Binghamton, NY 13902-6000 USA
Jean Pedersen
Affiliation:
Department of Mathematics & CS, Santa Clara University, Santa Clara, CA 95053-0290 USA, e-mail: jpedersen@scu.edu
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Extract

Dedicated to the memory of Russell Towle, a remarkable man who contributed so much to geometry and to other aspects of the quality of life.

We introduce an expanded notation where r + s = n, for the binomial coefficient , and then use this expanded notation to develop theorems involving 8 binomial coefficients, analogous to the Star of David Theorem, which. in its original form, involved the 6 neighbours of a given binomial coefficient in the Pascal Triangle (see Section 3), that appeared in [1,2,3,4,5,6,7,8,9].

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Type
Articles
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The Mathematical Gazette , Volume 94 , Issue 530 , July 2010, pp. 247 - 261
Copyright
Copyright © The Mathematical Association 2010

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Footnotes

*

The material in this article was presented by the second author at the eighth Gathering for Gardner Conference (G4G8), in Atlanta, GA on 29 March 2008.

References

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