Geodesic
The Solution to a Problem of Grünbaum
Canadian mathematical bulletin, Tome 31 (1988) no. 2, pp. 129-138

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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 M min(k) and M max(k) are assumed with the exception of M max — 1 and M max — 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.
DOI : 10.4153/CMB-1988-020-2
Mots-clés : 05-A15 
Salamon, Peter; Erdös, Paul. The Solution to a Problem of Grünbaum. Canadian mathematical bulletin, Tome 31 (1988) no. 2, pp. 129-138. doi: 10.4153/CMB-1988-020-2
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     author = {Salamon, Peter and Erd\"os, Paul},
     title = {The {Solution} to a {Problem} of {Gr\"unbaum}},
     journal = {Canadian mathematical bulletin},
     pages = {129--138},
     year = {1988},
     volume = {31},
     number = {2},
     doi = {10.4153/CMB-1988-020-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-020-2/}
}
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