Fibonacci-based generalizations of degenerate Stirling numbers

Dişkaya, Orhan

This paper introduces and systematically investigates Fibonacci-based analogues and generalizations of degenerate Stirling and Lah numbers. We begin by recalling the classical definitions and key properties of Stirling numbers of both kinds, Lah numbers, Fibonacci numbers, and Fibonomial coefficients, along with F-falling and F-rising factorials. The foundational concept of degenerate numbers and their associated degenerate factorials, as initiated by Carlitz, is also reviewed. Our primary contribution is the definition of four new families of numbers: the degenerate F-Stirling numbers of the first kind and S1,λF(n,k), the degenerate F-Stirling numbers of the second kind S2,λF(n,k), and the degenerate F-Lah number LλF(n,k). These numbers are precisely characterized as connection coeffici...