Shigeki Akiyama

activity

20242026

collaborators

6 papers

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.NT2025

Discretized Rotation with fixed initial points

Shigeki Akiyama, Bill Mance

We prove that if $max {∣ a_{0} ∣, ∣ a_{1} ∣} \leq 10$ and $λ \in] - 2, 2 [$ , then the sequence defined by $0 \leq a_{n + 2} + λ a_{n + 1} + a_{n} < 1$ is periodic.

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.NT2025

Dynamical systems defined by polynomials with algebraic properties

Shigeki Akiyama, Xiang Gao, Teturo Kamae

Let (x_n; n\in Z) be a bisequence of elements x_n in the 1-dimensional torus R/Z, which is called a stream over R/Z. Let P(z)=a_k z^k+...+a_1 z+a_0 be a polynomial with integer coe…

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…

math.NT2024

Delone sets associated with badly approximable triangles

Shigeki Akiyama, Emily R. Korfanty, Yanli Xu

We construct new Delone sets associated with badly approximable numbers which are expected to have rotationally invariant diffraction. We optimize the discrepancy of corresponding…