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Coassociative grammar, periodic orbits, and quantum random walk over ℤ

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Figure

Figure 3.1. Combinatorics from the quantum random walk over Z, up to t = 3.
Figure 4.1. Path associated with PPPQP.
Figure 4.2. The quantum random walk, coded in terms of the path space �.
Figure 4.3. Periodic orbit, ⟨a ⊗b ⊗c⟩, with pattern of length 3.
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