2025/10/30 by Aleks Žigon Tankosič, Tankosič, Aleks Žigon
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #General Mathematics (math.GM)
paper · pdf · doi:10.48550/arxiv.2510.26842
openalex publication_date 2025/10/30 · openalex created_date 2025/11/05 · openalex updated_date 2026/07/28
In this paper we introduce and study two generalizations of Lah numbers, analogous to the Stirling numbers with higher level - a combinatorial one (Lah numbers with higher level) and an algebraic one (Lah numbers of order s). We define the Lah numbers with higher level following a combinatorial approach and the Lah numbers of order s following an algebraic approach. We prove a direct connection between the Lah numbers with higher level and the (l,r)-Lah numbers. Some properties of the Lah numbers of order s and Lah polynomials of order s are given. Finally, we prove connections between these two generalizations.