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math.NT2024
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.CO2024
Connections between certain numbers related to derangements and -permutations
Piotr Miska, Błażej Żmija
For non-negative integer parameters define \begin{align*} \cal{D}(r,u,m,n) := \big\{\ σ\in \cal{S}_{r+n}\ \big|\ σ(x)=y \textrm{ for exactly } u \textrm{ pairs } (x,y) \t…
math.NT2024
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\…