4 citations · 4 across the 7 of their papers we have counts for
7 papers
On the monoid of lexicographically minimal extensions
Jonathan Caalim, Yu-ichi Tanaka
A sequence of nonnegative integers , where or , is called a binomid index if for a…
An analogue of Solomyak's theorem for periodic Cantor real expansions in alternate bases
Jonathan Caalim, Nathaniel Nollen
In this paper, we consider the positional numeration system, called the Cantor real expansion, on the unit interval , where , with respect to an alternat…
Rotational beta expansions and Schmidt games
Hajime Kaneko, Jonathan Caalim, Nathaniel Nollen
We consider rotational beta expansions in dimensions 1, 2 and 4 and view them as expansions on real numbers, complex numbers, and quaternions, respectively. We give sufficient cond…
Isometric and selfadjoint operators on a vector space with nondegenerate diagonalizable form
Jonathan V. Caalim, Vyacheslav Futorny, Vladimir V. Sergeichuk +1
Let be a vector space over a field with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If ,…
Corona limits of tilings : Periodic case
Shigeki Akiyama, Jonathan Caalim, Katsunobu Imai +1
We study the limit shape of successive coronas of a tiling, which models the growth of crystals. We define basic terminologies and discuss the existence and uniqueness of corona li…
Invariant measure of rotational beta expansion and a problem of Tarski
Shigeki Akiyama, Jonathan Caalim
We study invariant measures of a piecewise expanding map in defined by an expanding similitude modulo lattice. Using the result of Bang on a problem of Tarski, we sh…