Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1

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
D-33615 Germany


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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