- Title
- Growth degree classification for finitely generated semigroups of integer matrices
- Creator
- Bell, Jason P.; Coons, Michael; Hare, Kevin G.
- Relation
- ARC.DE140100223 http://purl.org/au-research/grants/arc/DE140100223
- Relation
- Semigroup Forum Vol. 92, Issue 1, p. 23-44
- Publisher Link
- http://dx.doi.org/10.1007/s00233-015-9725-1
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2016
- Description
- Let A be a finite set of d x d matrices with integer entries and let mn(Α) be the maximum norm of a product of n elements of A. In this paper, we classify gaps in the growth mn(Α); specifically, we prove that limn→∞log mn(A)/log n ∈ℤ≥₀⋃{∞}. This has applications to the growth of regular sequences as defined by Allouche and Shallit.
- Subject
- finitely generated semigroups; matrix semigroups; automatic sequences; regular sequences
- Identifier
- http://hdl.handle.net/1959.13/1319649
- Identifier
- uon:23925
- Identifier
- ISSN:0037-1912
- Language
- eng
- Reviewed
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