B. Sobolewski

activity

20172026

most citedValues of binary partition function represented by a sum of three squares

1 citations · 1 across the 10 of their papers we have counts for

collaborators

12 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.NT2024

On the behavior of binary block-counting functions under addition

Bartosz Sobolewski

Let $s (n)$ denote the sum of binary digits of an integer $n \geq 0$ . In the recent years there has been interest in the behavior of the differences $\mathsf{s}(n+t)-\maths…

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

Decomposing the sum-of-digits correlation measure

Bartosz Sobolewski, Lukas Spiegelhofer

Let $s (n)$ denote the number of ones in the binary expansion of the nonnegative integer $n$ . How does $s$ behave under addition of a constant $t$ ? In order to study the differences…

math.NT2023

Block occurrences in the binary expansion

Bartosz Sobolewski, Lukas Spiegelhofer

The binary sum-of-digits function $s$ returns the number of ones in the binary expansion of a nonnegative integer. Cusick's Hamming weight conjecture states that, for all…

math.NT2022★ 1 cited

Values of binary partition function represented by a sum of three squares

Bartosz Sobolewski, Maciej Ulas

Let $m$ be a positive integer and $b_{m} (n)$ be the number of partitions of $n$ with parts being powers of 2, where each part can take $m$ colors. We show that if $m = 2^{k} - 1$ , then…