The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given n points and m lines in the Euclidean...

including Szemerédi's theorem, the Szemerédi regularity lemma, the Erdős–Szemerédi theorem, the Hajnal–Szemerédi theorem and the Szemerédi–Trotter theorem. Szemerédi...

set of points and the lines they determine is given by: Theorem (Szemerédi–Trotter): given n points and m lines in the plane, the number of flags (incident...

only the Szemerédi–Trotter theorem extend automatically to the complex numbers, since the Szemerédi-Trotter theorem holds over ℂ2 by a theorem of Tóth...

O(n^{4/3})} on the total number of point-line incidences given by the Szemerédi–Trotter theorem. Hopcroft's problem is named after John Hopcroft, who posed it...

{\displaystyle 2^{j+1}-1} points of P (including A and B). From the Szemerédi–Trotter theorem, the number of such lines is O ( n 2 / 2 3 j + n / 2 j ) {\displaystyle...

limit theorems (mathematical analysis) Szemerédi's theorem (combinatorics) Szemerédi–Trotter theorem (combinatorics) Szpilrajn extension theorem (axiom...

areas of combinatorics, such as the Szemerédi–Trotter theorem and Chvátal-Rödl-Szemerédi-Trotter theorem. Trotter is the author of the book Combinatorics...

very simple proofs of some important theorems in incidence geometry. For instance, the Szemerédi–Trotter theorem, an upper bound on the number of incidences...

the Szemerédi–Trotter theorem provides a tighter O ( n 2 / 3 m 2 / 3 + n + m ) {\displaystyle O(n^{2/3}m^{2/3}+n+m)} bound. However, the Szemerédi–Trotter...

(m^{2/3}n^{2/3}+n)} , almost the same bound as occurs in the Szemerédi–Trotter theorem on point-line incidences in the plane. A simple proof of this...

the Szemerédi–Trotter theorem for lines in the complex plane.[HD] He has also contributed improved bounds for the Erdős–Szemerédi theorem, showing that...

simple proofs of some important theorems in incidence geometry, such as Beck's theorem and the Szemerédi-Trotter theorem, and Tamal Dey used it to prove...

Particularly notable was his "ingenious" application of the Szemerédi–Trotter theorem to improve the best known lower bound for the sum-product problem...

closely related to the crossing number inequality and to the Szemerédi–Trotter theorem on incidences between points and lines. For small values of n...

Cauchy–Schwarz inequality, the crossing number inequality, the Szemerédi–Trotter theorem on incidences between points and lines, and methods from information...

has been used to give a new proof of the Szemerédi–Trotter theorem via the polynomial ham sandwich theorem and has been applied to a variety of problems...

Thrm. 2.1 1994, Thrm. 2.2 Paul Wolfgang, Nick Pippenger, Endre Szemerédi, William Trotter. On determinism versus non-determinism and related problems. 24th...

numbers have a positive density? Determine growth rate of rk(N) (see Szemerédi's theorem) Class number problem: are there infinitely many real quadratic number...

1006/jctb.1993.1012, MR 1198403. Chvátal, Václav; Rödl, Vojtěch; Szemerédi, Endre; Trotter, William T. Jr. (1983), "The Ramsey number of a graph with bounded...