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We study colorings of regular trees using subball complex- ity b(n), which is the number of colored n-balls up to color-preserving isomorphisms. We show that for any k-regular tree, for k > 1, there are colorings of intermediate complexity. We then construct colorings of linear complexity b(n) = 2n + 2. We also construct colorings induced from sequences of linear subword complexity which has exponential subball complexity.
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참고문헌 (9)
참고문헌 신청
D. Kim / 2015 / Subword complexity and Sturmian colorings of regular trees / Ergodic Theory Dynam. Systems 35 (2) : 461 ~ 481
E. Coven / 1973 / Sequences with Minimal Block Growth / Math. Systems Theory 7 : 138 ~ 153
G. Rote / 1994 / Sequences with Subword complexity 2n / J. Number Theory 46 (2) : 196 ~ 213
H. Bass / 2001 / Tree Lattices / Birkhauser
J. Cassaigne / 2003 / Constructing in nite words of intermediate complexity, Developments in language theory / Lecture Notes in Comput. Sci. 2450 : 173 ~ 184
E. Coven / 1973 / Sequences with Minimal Block Growth / Math. Systems Theory 7 : 138 ~ 153
G. Rote / 1994 / Sequences with Subword complexity 2n / J. Number Theory 46 (2) : 196 ~ 213
H. Bass / 2001 / Tree Lattices / Birkhauser
J. Cassaigne / 2003 / Constructing in nite words of intermediate complexity, Developments in language theory / Lecture Notes in Comput. Sci. 2450 : 173 ~ 184
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