Degenerate Euler-Seidel Matrix Method and Their Applications

TL;DR

This paper develops a degenerate Euler-Seidel matrix method with a parameter lambda, enabling new combinatorial identities and transformations for sequences such as degenerate Bell and Fubini numbers.

Contribution

It introduces a generalized Euler-Seidel matrix method incorporating a lambda parameter, expanding the classical approach with new identities and applications.

Findings

Derived new combinatorial identities for degenerate Bell numbers

Established transformation formulas using lambda-generalized binomial identities

Applied the method to generate identities for degenerate Fubini numbers

Abstract

This paper introduces a degenerate version of the Euler-Seidel matrix method by incorporating a parameter lambda into the classical recurrence relation. The standard Euler-Seidel method relates the generating functions of an initial sequence and its final sequence via Seidel's formula, Our generalized method establishes transformation formulas using lambda-generalized binomial identities and yields a degenerate Seidel's formula for the exponential generating functions. The results are applied to study and derive new combinatorial identities for sequences like the degenerate Bell and Fubini numbers and polynomials.