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Research Article Open access CC BY 4.0

On the Translated Whitney Numbers and their Combinatorial Properties

Mahid M. Mangontarum, Amerah M. Dibagulun

Current Journal of Applied Science and Technology · pp. 1–15 · Published 6 Sep 2015

10.9734/BJAST/2015/19973

Abstract

In this paper, we further develop the study of the translated Whitney numbers by deriving more combinatorial properties such as more recurrence relations, exponential and rational generating functions and the orthogonality and inverse relations. To achieve this goal, we introduce the “signed” translated Whitney numbers of the first kind. A relationship between these numbers and the Bernoulli polynomials is also briefly discussed.

Translated whitney numbers whitney numbers stirling numbers

References (5)

  1. 1 A New Formula for the Bernoulli Polynomials [DOI]
  2. 2 On Whitney numbers of Dowling lattices [DOI]
  3. 3 The r-Bell numbers
  4. 4 Translated Whitney and r-Whitney Numbers: A Combinatorial Approach
  5. 5 The Translated Dowling Polynomials and Numbers [DOI]

Cited by 9

On the Unified Generalized $q$-Stirling Matrices and Their Matrix Decompositions

Amerah Dibagulun, Charles B. Montero, M. M. Mangontarum · 2026

Bivariate extension of the r-Dowling polynomials and two forms of generalized Spivey’s formula

M. M. Mangontarum · Indian journal of pure and applied mathematics · 2022

Bivariate Extension of the r-Dowling Polynomials and the Generalized Spivey's Formula

M. M. Mangontarum · 2020

On Noncentral Tanny-Dowling Polynomials and Generalizations of Some Formulas for Geometric Polynomials

M. M. Mangontarum, Norlailah M. Madid · 2020

The translated Whitney–Lah numbers: generalizations and q-analogues

M. M. Mangontarum · 2020

Some Generalizations of Spivey's Bell Number Formula

M. M. Mangontarum, Amerah Dibagulun · 2017

Some Theorems and Applications of the (q, r)-Whitney Numbers

M. M. Mangontarum · Journal of Integer Sequences · 2017

A Note on the Translated Whitney Numbers and Their q-Analogues

M. M. Mangontarum, Omar I. Cauntongan, Amerah Dibagulun · 2016

The Noncentral Version of the Whitney Numbers: A Comprehensive Study

M. M. Mangontarum, Omar I. Cauntongan, Amila P. Macodi-Ringia · International Journal of Mathematics and Mathematical Sciences · 2016

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