Description of normal bases of boundary algebras and factor languages of slow growth
- 17 Downloads
For an algebra A, denote by V A (n) the dimension of the vector space spanned by the monomials whose length does not exceed n. Let T A (n) = V A (n) − V A (n − 1). An algebra is said to be boundary if T A (n) − n < const. In the paper, the normal bases are described for algebras of slow growth or for boundary algebras. Let L be a factor language over a finite alphabet A. The growth function T L (n) is the number of subwords of length n in L. We also describe the factor languages such that T L (n) ≤ n + const.
Keywordsnormal basis Sturm sequence growth function monomial algebra factor language
Unable to display preview. Download preview PDF.
- 1.A. Ya. Belov, V. V. Borisenko, and V. N. Latyshev, “Monomial algebras,” in Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., Contemporary Mathematics and Its Applications. Thematic Surveys, Vol. 26: Algebra 4 (VINITI, Moscow, 2002), pp. 35–214 [J. Math. Sci. (NewYork) 87 (3), 3463–3575 (1997)].Google Scholar
- 2.M. Lothaire, “Combinatorics on Words,” in Encyclopedia of Math. Appl. (Addison-Wesley, Reading, MA, 1983), Vol. 17.Google Scholar
- 3.G. M. Bergman, A Note on Growth Functions of Algebras and Semigroups, Research Note (University of California, Berkeley, CA, 1978).Google Scholar
- 4.J. Berstel and P. Séébold, “Sturmian words,” in Algebraic Combinatorics onWords, Encyclopedia ofMath. Appl. (Cambridge Univ. Press, Cambridge, 2002), Vol. 90.Google Scholar