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math.CO2026
Aperiodic tile sets from Sturmian lattices
Shigeki Akiyama, Tadahisa Hamada, Katsuki Ito
We give an explicit algorithm to construct aperiodic tile sets based on Sturmian words of quadratic slopes. The method works for any quadratic irrational slope, and we can produce…
math.CO2025
Sturmian lattices and Aperiodic tile sets
Shigeki Akiyama, Tadahisa Hamada, Katsuki Ito
We give an explicit algorithm to construct aperiodic tile sets based on Sturmian words of quadratic slopes. The method works for any quadratic irrational slope, and we can produce…
math.CO2024
3 dimensional Wythoff Nim
Shigeki Akiyama
We introduce a new generalization of Wythoff Nim using three piles of stones. We show that its P-positions have finite difference properties and produce a partition of positive int…