Geodesic
Into how many regions do $n$ lines divide the plane if at most $n-k$ of them are concurrent?
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2010), pp. 32-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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A number of connective components of the real projective plane, disjoint with the family of $n\geq 2$ distinct lines is estimated provided at most $n-k$ lines are concurrent. If $n\geq\frac{k^2+k}2+3$, then the number of regions is at least $(k+1)(n-k)$. Thus, a new proof of Martinov's theorem is obtained. This theorem determines all pairs of integers $(n,f)$ such that there is an arrangement of $n$ lines dividing the projective plane into $f$ regions. 
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     author = {I. N. Shnurnikov},
     title = {Into how many regions do $n$ lines divide the plane if at most $n-k$ of them are concurrent?},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {32--36},
     year = {2010},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_5_a5/}
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I. N. Shnurnikov. Into how many regions do $n$ lines divide the plane if at most $n-k$ of them are concurrent?. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2010), pp. 32-36. http://geodesic.mathdoc.fr/item/VMUMM_2010_5_a5/