12 citations · 65 across the 36 of their papers we have counts for
4 papers · 1 filter
The computation of overlap coincidence in Taylor-Socolar substitution tiling
Shigeki Akiyama, Jeong-Yup Lee
Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tiling can be viewed as a substitution tiling. We use the substitution rule for this tiling and apply…
Mean Divisibility of Multinomial coefficients
Shigeki Akiyama
Let m_1,...,m_s be positive integers. Consider the sequence defined by multinomial coefficients: a_n=\binom{(m_1+m_2+... +m_s)n}{m_1 n, m_2 n,..., m_s n}. Fix a positive integer k\…
Discretized rotation has infinitely many periodic orbits
Shigeki Akiyama, Attila Pethoe
For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.
Comments on the height reducing property
Shigeki Akiyama, Toufik Zaimi
A complex number alpha is said to satisfy the height reducing property if there is a finite subset F of the ring Z of the rational integers such that Z[alpha]=F[alpha]. This proble…