Distinct distances between points and lines in Fq2

被引：4

作者：

Thang Pham ^{[1
]}

Nguyen Duy Phuong ^{[2
]}

Nguyen Minh Sang ^{[2
]}

Valculescu, Claudiu ^{[1
]}

Le Anh Vinh ^{[3
]}

机构：

[1] EPF Lausanne, Dept Math, Lausanne, Switzerland

[2] Vietnam Natl Univ, Hanoi Univ Sci, Hanoi, Vietnam

[3] Vietnam Natl Univ, Univ Educ, Hanoi, Vietnam

来源：

FORUM MATHEMATICUM | 2018年 / 30卷 / 04期

基金：

瑞士国家科学基金会;

关键词：

Distinct distances; point-line incidences; finite fields; SUM-PRODUCT ESTIMATE; FINITE-FIELDS; SPACES;

D O I：

10.1515/forum-2016-0248

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that if we are given a set of points P and set of lines L in F-q(2) such that vertical bar P parallel to|L vertical bar >= q(8/3), then the set of distinct distances between points from P and lines from L contains a positive proportion of all distances. Using the same techniques, we also obtain a generalization of this result in higher dimensional cases.

引用

页码：799 / 808

页数：10

共 50 条

[41] Few distinct distances implies no heavy lines or circles
Sheffer, Adam
Zahl, Joshua
de Zeeuw, Frank
COMBINATORICA, 2016, 36 (03) : 349 - 364
[42] SUMS OF DISTANCES BETWEEN POINTS ON A SPHERE
STOLARSKY, KB
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 35 (02) : 547 - +
[43] SUM OF DISTANCES BETWEEN POINTS ON A SPHERE
ALEXANDER, R
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1972, 23 (3-4): : 443 - 448
[44] Extended distances between fuzzy points
Casasnovas, J.
Riera, J. Vicente
NEW DIMENSIONS IN FUZZY LOGIC AND RELATED TECHNOLOGIES, VOL II, PROCEEDINGS, 2007, : 163 - 168
[45] About Distances between Points on the Plane
S. V. Konyagin
Mathematical Notes, 2001, 69 : 578 - 581
[46] Few distinct distances implies no heavy lines or circles
Adam Sheffer
Joshua Zahl
Frank de Zeeuw
Combinatorica, 2016, 36 : 349 - 364
[47] Hermitian dual-containing constacyclic codes over Fq2 + v1Fq2 + ... + vrFq2 and new quantum codes
Wang, Yu
Kai, Xiaoshan
Sun, Zhonghua
Zhu, Shixin
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2023, 15 (01): : 145 - 158
[48] Hermitian LCD codes over Fq2 + uFq2 and their applications tomaximal entanglement EAQECCs
Xu, Heqian
Du, Wei
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2022, 14 (02): : 259 - 269
[49] Lattice Codes Based on Product Constructions over Fq2 with Applications to Compute-and-Forward
Huang, Yu-Chih
Narayanan, Krishna R.
2013 IEEE INFORMATION THEORY WORKSHOP (ITW), 2013,
[50] Constructions of MDS, Near MDS and Almost MDS Codes From Cyclic Subgroups of Fq2*
Heng, Ziling
Li, Chengju
Wang, Xinran
IEEE TRANSACTIONS ON INFORMATION THEORY, 2022, 68 (12) : 7817 - 7831

← 1 2 3 4 5 →