# Chains and fixing blocks in irreducible binary sequences

Article

3-1985

## Department

Department of Mathematical Sciences; Department of Computer Science

## Abstract

A fixing block in an irreducible word is a square, segment of the form XX, and the period is the length of X. An occurrence of a block C in an irreducible word, W = XCY, is called a chain if XA having an infinite irreducible extension implies A is an initial segment of C. The length of such a chain is the length of C. It is shown that every fixing block has period equal 2k or 3(2k), and fixing blocks are produced having these periods. To each of these fixing blocks is associated a chain. The length of the chain which corresponds to the fixing block with period 2k is 3(2k-1)-1, and the length of the chain which corresponds to the fixing block of length 3(2k) is 2k+2-1. Moreover, these chains occur in words which contain no square longer than the associated fixing block.

## Publication Title

Discrete Mathematics

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