Szabó-Gyimesi Eszter (University of Debrecen): Associated $r$-Dowling numbers and some relatives

Number Theory and Algebra Seminar (Debrecen)

Abstract: In our talk, we introduce and study a new generalization of Bell numbers by combining $r$-Bell numbers, associated Bell numbers and Dowling numbers. For defining these $s$-associated $r$-Dowling numbers, we partition elements into blocks so that $r$ distinguished elements have to be in distinct blocks, the cardinality of certain blocks is bounded from below by $s$, and some elements are coloured according to a colouring rule. Along with them, we also define and investigate some relatives, the $s$-associated $r$-Dowling factorials and the $s$-associated $r$-Dowling--Lah numbers, when the underlying set is decomposed into cycles or ordered blocks.