19 papers · 1 filter
On the arithmetic of multidimensional continued fractions
Piotr Miska, Nadir Murru, Giuliano Romeo
The problem of developing an arithmetic for continued fractions (in order to perform, e.g., sums and products) does not have a straightforward solution and has been addressed by se…
Binary sequences meet the Fibonacci sequence
Piotr Miska, Bartosz Sobolewski, Maciej Ulas
We introduce a new family of meta-Fibonacci sequences , governed by the recurrence relation where $\mathbf{u}=(u_{n})…
On practical sets and -practical numbers
Andrzej Kukla, Piotr Miska
Let be a set of positive integers. We define a positive integer as an -practical number if every positive integer from the set $\left\{1,\ldots ,\sum_{d\in A, d\mid n}d\…
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…
On alternative definition of Lucas atoms and their -adic valuations
Gessica Alecci, Piotr Miska, Nadir Murru +1
Lucas atoms are irreducible factors of Lucas polynomials and they were introduced in \cite{ST}. The main aim of the authors was to investigate, from an innovatory point of view, wh…
Characteristics of distributions of sets and their - and -denseness
Piotr Miska, János T. Tóth
Let and denotes the set of all positive integers. In this paper we will deal with it too the family of all regularly distributed set…