Certain sequences of Wythoffian matrices, and maximal geometric progressions therein
type: Item
instance of: scholarly article
title: Certain sequences of Wythoffian matrices, and maximal geometric progressions therein
zbMATH Open document ID: 0814.05069
DOI: 10.1016/0097-3165(94)90111-2
published in: Journal of Combinatorial Theory. Series A
publication date: 1994-11-30T00:00:00Z
review text: Van der Waerden's Theorem states that if the positive integers are partitioned in two classes then at least one of the classes must contain arbitrary long arithmetic progressions. Several authors extended this theorem to establish the existence of long arithmetic progressions in different classes of ``not too thin'' sets of positive integers. Since the (additive) group \(\mathbb{Z}\) of integers can be represented (multipicatively) through a subgroup of \(\text{Gl}_ 2(\mathbb{Z})\) one further extension of van der Waerden type problems is the study of geometric progressions in subsets of \(\text{Gl}_ 2(\mathbb{Z})\). For a particular subset arising naturally in the study of winning pairs for ``Wythoff's Nim'' the author determines the distribution of maximal geometric progressions.
reviewed by: Joachim Rosenthal
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 11B25
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 20M99
zbMATH DE Number: 679881
zbMATH Keywords: sequences
zbMATH Keywords: Wythoffian matrices
zbMATH Keywords: Wythoff pairs
zbMATH Keywords: van der Waerden's theorem
zbMATH Keywords: Ramsey theory
zbMATH Keywords: Fibonacci numbers
zbMATH Keywords: arithmetic progressions
zbMATH Keywords: geometric progressions
author: Kenneth B. Stolarsky
MaRDI profile type: Publication
full work available at URL: 0097-3165(94)90111-2
OpenAlex ID: W2030985108
cites work: Q3944542
cites work: Characterization of the set of values \(f(n)=[n \alpha ], n=1,2,\dots \)
cites work: Q3351453
cites work: Q3997075
cites work: Fibonacci multiplication
cites work: Q3481787
cites work: Half-Silvered Mirrors and Wythoff's Game
cites work: Beatty Sequences, Continued Fractions, and Certain Shift Operators
cites work: Positive factors of Wythoff matrices
description: scientific article; zbMATH DE number 679881