Generalized r-Lah numbers

2014/12/30 by Mark Shattuck, Shattuck, Mark · 1 citation
Mathematics · #05A18 #05A19 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A18 #msc:05A19

paper · pdf · doi:10.48550/arxiv.1412.8721

arxiv created 2014/12/30 · arxiv updated 2014/12/31

Abstract

In this paper, we consider a two-parameter polynomial generalization, denoted by 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 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 identities involving the r-Lah numbers which were established previously using algebraic methods. Generalizing these arguments yields orthogonality-type relations that are satisfied by G_a,b(n,k;r).

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