A complete categorization of when generalized Tribonacci sequences can be avoided by additive partitions
type: Item
instance of: scholarly article
title: A complete categorization of when generalized Tribonacci sequences can be avoided by additive partitions
zbMATH Open document ID: 0964.05008
author: Mike Develin
published in: The Electronic Journal of Combinatorics
publication date: 2000-11-30T00:00:00Z
full work available at URL: https://eudml.org/doc/121047
full work available at URL: v7i1r53.html
review text: Let \(C\) be a set of positive integers. \(C\) is said to be avoidable if there is a partition of \(\mathbb{N}\) into two parts \(A\) and \(B\) such that \(A+B\cap C=\emptyset\), where \(A+B=\{a+b \mid a\in A\), \(b\in B\}.\) For example the Fibonacci sequence is avoidable as Alladi, Erdős and Hoggatt proved. Hoggatt, and later Dumitru, investigated the sequence with recursion \(s_n=s_{n-1}+s_{n-2}+s_{n-3}\) and special initial terms. In the present paper the author investigates the case when the initial terms are arbitrary. He establishes a finite set \(C\) showing that \(\{s_n\}\) is avoidable if and only if \(C\) is avoidable.
reviewed by: Norbert Hegyvári
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 1531354
zbMATH Keywords: avoidable set
zbMATH Keywords: additive partition
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1531354