On colouring integers avoiding \(t\)-AP distance-sets

• Date: 2016
• Main Author: Ahmed, Tanbir
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: distance sets; colouring integers; sets and sequences; 05D10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/78
• Journal Title: Algebra and Discrete Mathematics

A \(t\)-AP is a sequence of the form \(a,a+d,\ldots, a+(t-1)d\),where \(a,d\in \mathbb{Z}\). Given a finite set \(X\) and positive integers \(d\), \(t\), \(a_1,a_2,\ldots,a_{t-1}\), define \(\nu(X,d) = |\{(x,y):{x,y\in{X}},{y>x},{y-x=d}\}|\), \((a_1,a_2,\ldots,a_{t-1};d) =\) a collection \(X\...