Maciej Ulas

activity

20232026

collaborators

5 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

For an integer tuple $(a_{0}, a_{1}, \dots, a_{d})$ with $a_{i} \neq = 0$ for $i = 1, \dots, d$ , we define the associated Hilbert cube by \[ H(a_0;a_1,\ldots,a_d) = \left\{ a_0+\sum_{i=1}^d \vareps…

math.NT2024

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})…

math.NT2024

Signs behaviour of sums of weighted numbers of compositions

Filip Gawron, Maciej Ulas

Let $A$ be a subset of positive integers. For a given positive integer $n$ and $0 \leq i \leq n$ let $c_{A} (i, n)$ denotes the number of $A$ -compositions of $n$ with exactly $i$ parts…

math.NT2023

On general approach to Bessenrodt-Ono type inequalities and log-concavity property

Krystian Gajdzica, Piotr Miska, Maciej Ulas

In recent literature concerning integer partitions one can find many results related to both the Bessenrodt-Ono type inequalities and log-concavity property. In this note we offer…