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- Title
The Number of Configurations in the Full Shift with a Given Least Period.
- Authors
Castillo-Ramirez, Alonso; Sanchez-Alvarez, Miguel
- Abstract
For any group G and any set A, consider the shift action of G on the full shift A G . A configuration x ∈ A G has least period H ≤ G if the stabiliser of x is precisely H. Among other things, the number of such configurations is interesting as it provides an upper bound for the size of the corresponding Aut (A G) -orbit. In this paper, we show that if G is finitely generated and H is of finite index, then the number of configurations in A G with least period H may be computed by using the Möbius function of the lattice of subgroups of finite index in G. Moreover, when H is a normal subgroup, we classify all situations such that the number of G-orbits with least period H is at most 10.
- Subjects
MOBIUS function; SUBGROUP growth; FINITE, The
- Publication
Bulletin of the Iranian Mathematical Society, 2022, Vol 48, Issue 4, p1859
- ISSN
1018-6301
- Publication type
Article
- DOI
10.1007/s41980-021-00629-0