Measuring cones and other thick subsets in free groups
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 mono...
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University of Isfahan
2018-12-01
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| Series: | International Journal of Group Theory |
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| Online Access: | http://ijgt.ui.ac.ir/article_21479_33235e249efcf4f459180ac8cdea5176.pdf |
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doaj-7c4e93b30b6848848b2329b59c4b39402020-11-25T00:42:24ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692018-12-0174274010.22108/ijgt.2017.2147921479Measuring cones and other thick subsets in free groupsElizaveta Frenkel0Vladimir Remeslennikov1Moscow State UniversityMathematical Institute SB RASIn 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.http://ijgt.ui.ac.ir/article_21479_33235e249efcf4f459180ac8cdea5176.pdffree group$lambda-$measureregular subsetspecial automatonthick monoid |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Elizaveta Frenkel Vladimir Remeslennikov |
| spellingShingle |
Elizaveta Frenkel Vladimir Remeslennikov Measuring cones and other thick subsets in free groups International Journal of Group Theory free group $lambda-$measure regular subset special automaton thick monoid |
| author_facet |
Elizaveta Frenkel Vladimir Remeslennikov |
| author_sort |
Elizaveta Frenkel |
| title |
Measuring cones and other thick subsets in free groups |
| title_short |
Measuring cones and other thick subsets in free groups |
| title_full |
Measuring cones and other thick subsets in free groups |
| title_fullStr |
Measuring cones and other thick subsets in free groups |
| title_full_unstemmed |
Measuring cones and other thick subsets in free groups |
| title_sort |
measuring cones and other thick subsets in free groups |
| publisher |
University of Isfahan |
| series |
International Journal of Group Theory |
| issn |
2251-7650 2251-7669 |
| publishDate |
2018-12-01 |
| description |
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. |
| topic |
free group $lambda-$measure regular subset special automaton thick monoid |
| url |
http://ijgt.ui.ac.ir/article_21479_33235e249efcf4f459180ac8cdea5176.pdf |
| work_keys_str_mv |
AT elizavetafrenkel measuringconesandotherthicksubsetsinfreegroups AT vladimirremeslennikov measuringconesandotherthicksubsetsinfreegroups |
| _version_ |
1725282773353103360 |