Rácz Gabriella (University of Debrecen): The r-Fubini–Lah numbers and polynomials

Number Theory and Algebra Seminar (Debrecen)

Abstract: In our talk we define the r-Fubini–Lah numbers, which count those partitions of a finite set, where both the blocks and the partition itself are ordered, and r distinguished elements belong to distinct ordered blocks. In connection with these numbers, we introduce the r-Fubini–Lah polynomials, as well.
We give a detailed overview of the properties of the r-Fubini–Lah numbers and polynomials. We prove two recurrences and a Dobinski type formula for them, we derive the exponential generating function of their sequences, and we investigate how they are connected with the r-Fubini numbers and polynomials.