Some Identities Involving -Stirling Numbers of the Second Kind in Type B
Mingjian Ding, Jiang Zeng
Source abstract
The recent interest in type B -Stirling numbers of the second kind prompted us to give a type B analogue of a classical identity connecting the -Stirling numbers of the second kind and Carlitz's major -Eulerian numbers, which turns out to be a -analogue of an identity due to Bagno, Biagioli and Garber. We provide a combinatorial proof of this identity and an algebraic proof of a more general identity for colored permutations. In addition, we prove some -identities about the -Stirling numbers of the second kind in types A, B and D.
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