A Generalisation of a Result on Monotone Arithmetic Progressions in Permutations of the Positive Integers

2023/02/19 by Sarosh Adenwalla, Adenwalla, Sarosh
Computer Science · Engineering · Mathematics · #11B25 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2302.09662

openalex publication_date 2023/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A permutation of the positive integers avoiding monotone arithmetic progressions of length 4 with odd common difference was constructed in (LeSaulnier and Vijay, 2011). We generalise this result and show that for each k≥ 1, there exists a permutation of the positive integers that avoids monotone arithmetic progressions of length 4 with common difference not divisible by 2^k.

Related

• Avoiding Monotone Arithmetic Progressions in Permutations of Integers
• Forbidden arithmetic progressions in permutations of subsets of the integers
• On Permutations Avoiding Short Progressions
• Arithmetic progressions consisting of unlike powers
• Narrow arithmetic progressions in the primes