| Title: | Nonuniform lines on finite projective planes |
|---|
| Authors: | ID Markó, Ádám (Author) |
|---|
| Files: |  ADAM_Marko_2026.pdf (414,61 KB)
MD5: 071A1B3D54B7ED188AC1A76376B11B99
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | ZUP - University of Primorska Press
|
|---|
| Abstract: | We consider the stability version of the following problem, originally posed by Erdős: colour the points of a projective plane of order q, q odd, with two colours. What is the minimum number of nonuniform lines, that is the lines on which the number of points of the two colours are not the same. It is easy to show that the number of nonuniform lines is at least q+1 and there is a trivial colouring with q+1 nonuniform lines. Our main result is that the number of nonuniform lines is at least 13/8 * q or we have the trivial colouring. |
|---|
| Keywords: | colouring, projective planes, blocking sets |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 01.12.2025 |
|---|
| Publisher: | Založba Univerze na Primorskem |
|---|
| Year of publishing: | 2026 |
|---|
| Number of pages: | 22 str. |
|---|
| Numbering: | Vol. 9, no. 1, [article no.] P1.08 |
|---|
| PID: | 20.500.12556/RUP-22823  |
|---|
| UDC: | 51 |
|---|
| eISSN: | 2590-9770 |
|---|
| DOI: | 10.26493/2590-9770.1803.58a |
|---|
| Publication date in RUP: | 20.03.2026 |
|---|
| Views: | 129 |
|---|
| Downloads: | 3 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
