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The Solution to a Problem of Grünbaum
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- Journal:
- Canadian Mathematical Bulletin / Volume 31 / Issue 2 / 01 June 1988
- Published online by Cambridge University Press:
- 20 November 2018, pp. 129-138
- Print publication:
- 01 June 1988
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- Article
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The paper characterizes the set of all possible values for the number of lines determined by n points for n sufficiently large. For
the lower bound of Kelly and Moser for the number of lines in a configuration with n — k collinear points is shown to be sharp and it is shown that all values between Mmin(k) and Mmax(k) are assumed with the exception of Mmax — 1 and Mmax — 3. Exact expressions are obtained for the lower end of the continuum of values leading down from 
In particular, the best value of c = 1 is obtained in Erdös’ previous expression 
for this lower end of the continuum.
the lower bound of Kelly and Moser for the number of lines in a configuration with 
In particular, the best value of 
for this lower end of the continuum.