Abstract
The solitaire of independence is a reversible process (more precisely, a groupoid/group action) resembling the classical 15-puzzle, which gives information about independent sets of coordinates in a totally extremally permutive subshift. We study the solitaire with the triangle shape, which corresponds to the spacetime diagrams of bipermutive cellular automata with radius 1/2. We give a polynomial time algorithm that puts any finite subset of the plane in normal form using solitaire moves, and show that the solitaire orbit of a line of consecutive ones – the line orbit – is completely characterised by the notion of a fill matrix. We show that the diameter of the line orbit under solitaire moves is cubic.
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Salo, V., Schabanel, J. (2023). Triangle Solitaire. In: Manzoni, L., Mariot, L., Roy Chowdhury, D. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2023. Lecture Notes in Computer Science, vol 14152. Springer, Cham. https://doi.org/10.1007/978-3-031-42250-8_9
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DOI: https://doi.org/10.1007/978-3-031-42250-8_9
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