A Szemerédi–Trotter type theorem, sum-product estimates in finite quasifields, and related results

http://repository.vnu.edu.vn/handle/VNU_123/28151

We prove a Szemerédi–Trotter type theorem and a sumproduct estimate in the setting of finite quasifields.

These estimates generalize results of the fourth author, of Garaev, and of Vu. We generalize results of Gyarmati and Sárközy on the solvability of the equations a + b = cd and ab + 1 = cd over a finite field.

Other analogous results that are known to hold in finite fields are generalized to finite quasifields.

Title:	A Szemerédi–Trotter type theorem, sum-product estimates in finite quasifields, and related results
Authors:	Pham Thang Tait, Michael Timmons, Craig Le Anh Vinh
Keywords:	Szemerédi–Trotter theorem Quasifield Sum-product estimate
Issue Date:	2017
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Citation:	ISIKNOWLEDGE
Abstract:	We prove a Szemerédi–Trotter type theorem and a sumproduct estimate in the setting of finite quasifields. These estimates generalize results of the fourth author, of Garaev, and of Vu. We generalize results of Gyarmati and Sárközy on the solvability of the equations a + b = cd and ab + 1 = cd over a finite field. Other analogous results that are known to hold in finite fields are generalized to finite quasifields.
Description:	TNS06969 ; JOURNAL OF COMBINATORIAL THEORY SERIES A Volume: 147 Pages: 55-74 Published: APR 2017
URI:	http://repository.vnu.edu.vn/handle/VNU_123/28151 1096-0899 http://www.sciencedirect.com/science/article/pii/S0097316516301169
ISSN:	0097-3165 1096-0899
Appears in Collections:	Bài báo của ĐHQGHN trong Web of Science