2017/07/24 by Florent Nguema Ndong, Ndong, Florent Nguema
Mathematics · #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1707.07730
Given a totally finite ordered alphabet A , endowing the set of words over A with the alternating lexicographic order, we define a new class of Lyndon words. We study the fundamental properties of the associated symbolic dynamical systems called Lyndon system. We derive some fundamental properties of the beta-shift with negative base by relating it with the Lyndon system. We find, independently of W. Steiner's method, the conditions for which a word is the (-β)-expansion of -\fracββ+ 1 for some β> 1.