3 papers
math.CO2021
The ordered Bell numbers as weighted sums of odd or even Stirling numbers of the second kind
Jacob Sprittulla
For the Stirling numbers of the second kind and the ordered Bell numbers , we prove the identity . An analogous identity ho…
math.CO2020
On Colored Factorizations
Jacob Sprittulla
We study the number of factorizations of a positive integer, where the parts of the factorization are of l different colors (or kinds). Recursive or explicit formulas are derived f…
math.CO2019
Unordered Factorizations with Parts
Jacob Sprittulla
We derive new formulas for the number of unordered (distinct) factorizations with parts of a positive integer as sums over the partitions of and an auxiliary function,…