Abstract
In this paper, we consider a two-parameter polynomial generalization, denoted by \(\mathcal {G}_{a,b}(n,k;r)\), of the r-Lah numbers which reduces to these recently introduced numbers when a = b = 1. We present several identities for \(\mathcal {G}_{a,b}(n,k;r)\) that generalize earlier identities given for the r-Lah and r-Stirling numbers. We also provide combinatorial proofs of some earlier identities involving the r-Lah numbers by defining appropriate sign-changing involutions. Generalizing these arguments yields orthogonality-type relations that are satisfied by \(\mathcal {G}_{a,b}(n,k;r)\).
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The author wishes to thank the referee for a careful reading of this paper and for questions posed that led to Theorems 2.4, 2.5 and 4.2.
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Communicating Editor: Parameswaran Sankaran
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SHATTUCK, M. Generalized r-Lah numbers. Proc Math Sci 126, 461–478 (2016). https://doi.org/10.1007/s12044-016-0309-0
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DOI: https://doi.org/10.1007/s12044-016-0309-0