Proceedings Mathematical Sciences | |
Generalized $r$-Lah numbers | |
MARK SHATTUCK1  | |
[1] $$ | |
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
【 预 览 】
Files | Size | Format | View |
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RO201912040507212ZK.pdf | 339KB | download |