Some identities involving q-Stirling numbers of the second kind in type B

2023/07/02 by Ding, Ming-Jian, Zeng, Jiang · 2 citations
#05A05 #05A18 #05A19 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.00570

Abstract

The recent interest in q-Stirling numbers of the second kind in type B 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 analytical 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.

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Related

• q-Stirling numbers in type B
• Combinatorics of q,r-analogues of Stirling numbers of type B
• Carlitz q-Bernoulli numbers and q-Stirling numbers
• q-Bernoulli numbers and Stirling numbers(2)
• Identities of Eulerain and ordered Stirling numbers over a multiset