2024/04/25 by Josef Küstner, Küstner, Josef
Chemistry · Mathematics · #05A15 #05E05 #11B65 #11B73 #11B83 #33E05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Primary 05A10 #Secondary 05A30
paper · pdf · doi:10.48550/arxiv.2404.16982
openalex publication_date 2024/04/25 · openalex created_date 2024/05/01 · openalex updated_date 2026/07/28
In this article we generalize the q-difference operator due to Carlitz in order to derive explicit sum formulae for several extensions of Stirling numbers of the second kind, including complete homogeneous symmetric functions, complementary symmetric functions, r-Whitney numbers and elliptic analogues of rook, Stirling and Lah numbers. Furthermore, we generalize Carlitz' q-Eulerian numbers to a Lagrange polynomial extension. We define them by generalizing Worpitzky's identity appropriately, and derive a recursion and an explicit sum formulae. Special cases include r-Whitney Eulerian numbers and elliptic Eulerian numbers.