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- W2620591744 abstract "Let $I(n,l)$ denote the maximum possible number of incidences between $n$ points and $l$ lines. It is well known that $I(n,l) = Theta(n^{2/3}l^{2/3} + n + l)$. Let $c_{mathrm{SzTr}}$ denote the lower bound on the constant of proportionality of the $n^{2/3}l^{2/3}$ term. The known lower bound, due to Elekes, is $c_{mathrm{SzTr}} ge 2^{-2/3} = 0.63$. With a slight modification of Elekes' construction, we show that it can give a better lower bound of $c_{mathrm{SzTr}} ge 1$, i.e., $I(n,l) ge n^{2/3}l^{2/3}$. Furthermore, we analyze a different construction given by Erd{H o}s, and show its constant of proportionality to be even better, $c_{mathrm{SzTr}} ge 3/(2^{1/3}pi^{2/3}) approx 1.11$." @default.
- W2620591744 created "2017-06-09" @default.
- W2620591744 creator A5052040348 @default.
- W2620591744 date "2017-05-31" @default.
- W2620591744 modified "2023-09-27" @default.
- W2620591744 title "The Constant of Proportionality in Lower Bound Constructions of Point-Line Incidences" @default.
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