scholarly journals Incidence Theorems and Their Applications

2012 ◽  
Vol 6 (4) ◽  
pp. 257-393 ◽  
Author(s):  
Zeev Dvir
Keyword(s):  
Incidence Theorems

Plane congruences of the second order in space of four dimensions and fifth incidence theorems

1932 ◽  
Vol 28 (3) ◽  
pp. 275-284 ◽  
Author(s):  
W. G. Welchman
Keyword(s):  
Second Order ◽  
Four Dimensions ◽  
Quartic Curve ◽  
Incidence Theorems

It is well known that the planes which meet four given lines in a space of four dimensions meet a fifth line, determined by the first four. Also the trisecant planes of a rational quartic curve in [4] which meet a line meet another rational quartic curve. These two theorems are of the same type and may conveniently be called “fifth incidence theorems”.

scholarly journals Geometric incidence theorems via Fourier analysis

2009 ◽  
Vol 361 (12) ◽  
pp. 6595-6611 ◽  
Author(s):  
Alex Iosevich ◽  
Hadi Jorati ◽  
Izabella Łaba
Keyword(s):  
Fourier Analysis ◽  
Incidence Theorems

scholarly journals Dimensional lower bounds for Falconer type incidence theorems

2019 ◽  
Vol 139 (1) ◽  
pp. 143-154
Author(s):  
Jonathan DeWitt ◽  
Kevin Ford ◽  
Eli Goldstein ◽  
Steven J. Miller ◽  
Gwyneth Moreland ◽  
...  
Keyword(s):  
Lower Bounds ◽  
Incidence Theorems

Additional note on plane congruences and fifth incidence theorems

1932 ◽  
Vol 28 (4) ◽  
pp. 416-420 ◽  
Author(s):  
W. G. Welchman
Keyword(s):  
Arbitrary Point ◽  
Second Order ◽  
Singular Points ◽  
Additional Note ◽  
Pass Through ◽  
Incidence Theorems ◽  
Incidence Theorem

In a recent paper I discussed plane congruences of order two in [4] and obtained congruences of types (2, 6)1, (2, 6)2, (2, 5), (2, 4) and (2, 3). The method employed was due to Segre, who showed that a plane congruence of order two in [4] has in general a curve locus of singular points which is met by each plane in five points. Then, if we can find a curve in [4], composite or not, with an ∞2 system of quadrisecant planes of which two pass through an arbitrary point, the planes must all meet a residual curve, and we shall have obtained a congruence of the second order and a fifth incidence theorem.

INCIDENCE CONSTRAINTS: A COMBINATORIAL APPROACH

2006 ◽  
Vol 16 (05n06) ◽  
pp. 443-460 ◽  
Author(s):  
DOMINIQUE MICHELUCCI ◽  
PASCAL SCHRECK
Keyword(s):  
Projective Plane ◽  
Computer Algebra ◽  
Geometric Constraints ◽  
Combinatorial Approach ◽  
Algebraic Systems ◽  
New Methods ◽  
Np Complete ◽  
Incidence Theorems

The simplest geometric constraints are incidences between points and lines in the projective plane. This problem is universal, in the sense that all algebraic systems reduce to such geometric constraints. Detecting incidence dependences between these geometric constraints is NP-complete. New methods to prove incidence theorems are proposed, which use strictly no computer algebra but only combinatorial arguments.

scholarly journals Generalized incidence theorems, homogeneous forms and sum–product estimates in finite fields

2010 ◽  
Vol 31 (1) ◽  
pp. 306-319 ◽  
Author(s):  
David Covert ◽  
Derrick Hart ◽  
Alex Iosevich ◽  
Doowon Koh ◽  
Misha Rudnev
Keyword(s):  
Finite Fields ◽  
Incidence Theorems
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