Maciej Ulas

collaborators

3 papers

math.NT2026

Hankel determinants of weighted binary sums of digits

Bartosz Sobolewski, Maciej Ulas

Let $s_{w}$ be the weighted binary sum-of-digits function associated with an arbitrary sequence of complex weights $w = (w_{j})_{j \geq 0}$ . We investigate Hankel determ…

math.NT2026

There are infinitely many Hilbert cubes of dimension 3 in the set of squares

Andrew Bremner, Christian Elsholtz, Maciej Ulas

A Hilbert cube of dimension $d$ is the set of integers \[ H(a_{0}; a_{1}, \ldots, a_{d})=a_{0}+\{0, a_{1}\}+\cdots+\{0, a_{d}\}=\left\{a_{0}+\sum_{i=1}^{d}\varepsilon_{i}a_{i}:\;\v…

math.NT2025

Binary sequences meet the Fibonacci sequence

Piotr Miska, Bartosz Sobolewski, Maciej Ulas

We introduce a new family of meta-Fibonacci sequences $(f (n))_{n \in N}$ , governed by the recurrence relation $f (n) = a f (n - u_{n} - 1) + b f (n - u_{n} - 2),$ where $\mathbf{u}=(u_{n})…