Generalized $r$-Lah numbers

Proceedings Mathematical Sciences

MARK SHATTUCK¹ 

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关键词: $r$-Lah numbers;    $r$-Stirling numbers;    polynomial generalization;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 ${mathcal G}_{a,b}(n, k; r)$.

【 授权许可】

Unknown