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Measuring cones and other thick subsets in free groups | ||
| International Journal of Group Theory | ||
| مقاله 4، دوره 7، شماره 4، اسفند 2018، صفحه 27-40 اصل مقاله (350.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21479 | ||
| نویسندگان | ||
| Elizaveta Frenkel* 1؛ Vladimir Remeslennikov2 | ||
| 1Moscow State University | ||
| 2Mathematical Institute SB RAS | ||
| چکیده | ||
| In this paper we investigate the special automata over finite rank free groups and estimate asymptotic characteristics of sets they accept. We show how one can decompose an arbitrary regular subset of a finite rank free group into disjoint union of sets accepted by special automata or special monoids. These automata allow us to compute explicitly generating functions, $\lambda-$measures and Cesaro measure of thick monoids. Also we improve the asymptotic classification of regular subsets in free groups. | ||
| کلیدواژه‌ها | ||
| free group؛ $lambda-$measure؛ regular subset؛ special automaton؛ thick monoid | ||
| مراجع | ||
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[13] M. O. Rabin and D. Scott, Finite automata and their decision problems, IBM J. Res. Develop., 3 no. 2 (1959) 114–125. | ||
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