2023/02/20 by Taekyun Kim, Kim, Taekyun, Dae San Kim +1
Computer Science · Mathematics · #11B73 #11B83 #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2302.09710
openalex publication_date 2023/02/20 · openalex created_date 2023/02/23 · openalex updated_date 2026/07/28
The Stirling numbers of the second kind are related to normal orderings in the Weyl algebra, while the unsigned Stirling numbers of the first kind are related to normal orderings in the shift algebra. Kim-Kim introduced a λ-analogue of the unsigned Stirling numbers of the first kind and that of the r-Stirling numbers of the first kind. In this paper, we introduce a λ-analogue of the shift algebra (called λ-shift algebra) and investigate normal orderings in the λ-shift algebra. From the normal orderings in the λ-shift algebra, we derive some identities about the λ-analogue of the unsigned Stirling numbers of the first kind .