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The recent interest in type B q-Stirling numbers of the second kind prompted us to give a type B analogue of a classical identity connecting the q-Stirling numbers of the second kind and Carlitz's major q-Eulerian numbers, which turns out to be a q-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 q-identities about the q-Stirling numbers of the second kind in types A, B and D.
Ding et al. (Fri,) studied this question.
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