Spivey-type recurrence relation for fully degenerate Bell polynomials

2025/09/06 by Taekyun Kim, Kim, Taekyun, Dae San Kim +1 · 1 citation
Computer Science · #11B73 #11B83 #Advanced Algebra and Logic #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2509.05761

openalex publication_date 2025/09/06 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

Spivey's combinatorial method revealed an important identity for Bell numbers, involving Stirling numbers of the second kind. This paper extends his work by deriving Spivey-type recurrence relations for fully degenerate Bell polynomials and degenerate Fubini polynomials. Our derivation uses degenerate Stirling numbers of the second kind and two-variable degenerate Fubini polynomials of order a.

Citations

• Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials
• Spivey's type recurrence relation for Lah-Bell polynomials
• Generalization of Spivey's recurrence relation
• Some results on degenerate Fubini and degenerate Bell polynomials
• Rook theoretic proofs of some identities related to Spivey's Bell number formula

Cited by

• A Generalized Recurrence for fully degenerate Bell polynomials

Related

• A Generalized Recurrence for fully degenerate Bell polynomials
• Spivey's type recurrence relation for degenerate Bell polynomials
• Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials
• Recurrence relations for degenerate Bell and Dowling polynomials via Boson operators
• Some identities related to degenerate r-Bell and degenerate Fubini polynomials