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arXiv · 2510.26842

The Lah Numbers with Higher Level and the Lah Numbers of Order s

Aleks Žigon Tankosič
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Abstract

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.

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Aleks Žigon Tankosič. 2025-10-30. The Lah Numbers with Higher Level and the Lah Numbers of Order s. https://arxiv.org/abs/2510.26842

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