COMBINATORIAL PROPERTIES OF POLY-BERNOULLI RELATIVES

摘要

In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show connections between the dierent areas where poly-Bernoulli numbers and their relatives appear and give examples of how the combinatorial methods can be used for deriving formulas between these integer arrays.