32 research outputs found
All Growth Rates of Abelian Exponents Are Attained by Infinite Binary Words
We consider repetitions in infinite words by making a novel inquiry to the maximum eventual growth rate of the exponents of abelian powers occurring in an infinite word. Given an increasing, unbounded function f: ? ? ?, we construct an infinite binary word whose abelian exponents have limit superior growth rate f. As a consequence, we obtain that every nonnegative real number is the critical abelian exponent of some infinite binary word
On k-abelian equivalence and generalized Lagrange spectra
We study the set of -abelian critical exponents of all Sturmian words. It has been proven that in the case this set coincides with the Lagrange spectrum. Thus the sets obtained when can be viewed as generalized Lagrange spectra. We characterize these generalized spectra in terms of the usual Lagrange spectrum and prove that when the spectrum is a dense non-closed set. This is in contrast with the case , where the spectrum is a closed set containing a discrete part and a half-line. We describe explicitly the least accumulation points of the generalized spectra. Our geometric approach allows the study of -abelian powers in Sturmian words by means of continued fractions.</p
45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
We consider repetitions in infinite words by making a novel inquiry to the maximum eventual growth rate of the exponents of abelian powers occurring in an infinite word. Given an increasing, unbounded function , we construct an infinite binary word whose abelian exponents have limit superior growth rate . As a consequence, we obtain that every nonnegative real number is the critical abelian exponent of some infinite binary word.</p