Multiple Bracket Function, Stirling Number, and Lah Number Identities

TL;DR

This paper develops multiple analogues of combinatorial numbers including the Lah numbers, and establishes identities and properties connecting these sequences, expanding the combinatorial framework.

Contribution

It introduces a multiple analogue of Lah numbers and derives new identities and properties linking all these combinatorial sequences.

Findings

Established a multiple analogue of Lah numbers.

Derived identities connecting various combinatorial sequences.

Analyzed properties of these new sequences.

Abstract

The author has constructed multiple analogues of several families of combinatorial numbers in a recent article, including the bracket symbol, and the Stirling numbers of the first and second kind. In the present paper, a multiple analogue of another sequence, the Lah numbers, is developed, and certain associated identities and significant properties of all these sequences are constructed.