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JCT
2008
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13 years 11 months ago
On the number of directions determined by a pair of functions over a prime field
A three-dimensional analogue of the classical direction problem is proposed and an asymptotically sharp bound for the number of directions determined by a nonplanar set in AG(3, p)...
Simeon Ball, András Gács, Pét...
EJC
2010
13 years 11 months ago
On the distance between the expressions of a permutation
Abstract. We prove that the combinatorial distance between any two reduced expressions of a given permutation of {1, ..., n} in terms of transpositions lies in O(n4), a sharp bound...
Patrick Dehornoy, Marc Autord
COMPGEOM
2005
ACM
14 years 1 months ago
Incidences of not-too-degenerate hyperplanes
We present a multi-dimensional generalization of the Szemer´edi-Trotter Theorem, and give a sharp bound on the number of incidences of points and not-too-degenerate hyperplanes i...
György Elekes, Csaba D. Tóth