3 papers
math.CO2025
Connections between certain numbers related to derangements and -permutations
Piotr Miska, BÅażej Å»mija
For non-negative integer parameters define \begin{align*} \cal{D}(r,u,m,n) := \big\{\ Ï\in \cal{S}_{r+n}\ \big|\ Ï(x)=y \textrm{ for exactly } u \textrm{ pairs } (x,y)…
math.NT2025
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})…
math.NT2025
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…