Chains and fixing blocks in irreducible binary sequences

✍ Scribed by R.O Shelton; R.P Soni

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 470 KB
• Volume: 54
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(85)90065-2

✦ Synopsis

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 irr~ucfole word, W = XCY, is called a chain if XA having an infinite/rreducible 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 2 k or 3(2 k), 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 2 k is 3(2k-I) -1, and the length of the chain which corresponds to the fixing block of length 3(2 k) is 2 k+2-1. Moreover, these chains occur in words which contain no square longer than the associated fixing block.