Computations for Symbolic Substitutions
Scott Balchin
Department of Mathematics
University of Leicester
University Road
Leicester, LE1 7RH
United Kingdom
Dan Rust
Department of Mathematics
Universität Bielefeld
Universitätsstraße
Bielefeld
D-33615 Germany
Abstract:
We provide a survey of results from symbolic dynamics and algebraic
topology relating to Grout, a new user-friendly program developed to
calculate combinatorial properties and topological invariants of a
large class of symbolic substitutions. We study their subshifts (and
related spaces) with an emphasis on examples of computations. We
implement a check to verify that no counterexample exists to the
so-called strong coincidence conjecture for a large number of
substitutions on three and four letters.
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(Concerned with sequences
A001285
A003842
A003849
A010059
A010060
A014577
A014709
A014710
A020985
A035263
A049320
A049321
A049472
A073057
A092782
A096268
A096270
A100260
A100619
A106665
A171588
A275202
A275855.)
Received July 22 2016; revised versions received August 24 2016; January 27 2017.
Published in Journal of Integer Sequences, January 27 2017.
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