Observations on de Bruijn graphs
Abstract of chapter 1 For n >= 2 the number of mixing n-step subshifts of finite type (sft) over the alphabet {0, 1} is proven to be at least 15/16 times the number of transitive n-step sfts. A conjecture assumes the latter to be at least 2^(3*2^(n-1)-n). Abstract of chapter 2 The alternating colouring function is defined. Strings over the alphabet {0, 1} are divided in colourable and non-colouraImagine an of characters A and B. Such can be thought of as a paper strip with As and Bs written on it, one end of which one holds in the hand while the other stretches over the horizon without ever ending. Or as a calculator that displays a new character each second. Or as a printer with an infinite amount of paper and ink that unfortunately only prints As and Bs. In contrast to infinite strings
