Scholarlink

Abstract <p>Spivey found a recurrence relation for the Bell numbers by using combinatorial method. The aim of this paper is to derive Spivey’s type recurrence relations for the degenerate Bell polynomials and the degenerate Dowling polynomials by using the boson annihilation and creation operators satisfying the commutation relation <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2302_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="107" /> </InlineMediaObject> <EquationSource Format="TEX">\(a{{a}^{ + }} - {{a}^{ + }}a = 1\)</EquationSource> <!--ComMat2570110Kim-m1--> </InlineEquation>. In addition, we derive a Spivey’s type recurrence relation for the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2302_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\)</EquationSource> <!--ComMat2570110Kim-m2--> </InlineEquation>-Dowling polynomials.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Recurrence Relations for Degenerate Bell and Dowling Polynomials via Boson Operators

  • 期刊论文

  • 发表日期：

    2025年9月1日

查看全文
  • Taekyun Kim,
  • Dae San Kim

摘要

Abstract

Spivey found a recurrence relation for the Bell numbers by using combinatorial method. The aim of this paper is to derive Spivey’s type recurrence relations for the degenerate Bell polynomials and the degenerate Dowling polynomials by using the boson annihilation and creation operators satisfying the commutation relation \(a{{a}^{ + }} - {{a}^{ + }}a = 1\) . In addition, we derive a Spivey’s type recurrence relation for the \(r\) -Dowling polynomials.