Complementary Bell Numbers: Arithmetical Properties and Wilf’s Conjecture

2013 ◽  
pp. 23-56
Author(s):  
Tewodros Amdeberhan ◽  
Valerio De Angelis ◽  
Victor H. Moll
Keyword(s):  
Bell Numbers ◽  
Wilf’S Conjecture

scholarly journals Complete and incomplete Bell polynomials associated with Lah–Bell numbers and polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Lee-Chae Jang ◽  
Hyunseok Lee ◽  
Han-Young Kim
Keyword(s):  
Bell Polynomials ◽  
Bell Numbers ◽  
Bell Number ◽  
Finite Sums

AbstractThe nth r-extended Lah–Bell number is defined as the number of ways a set with $n+r$ n + r elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to introduce incomplete r-extended Lah–Bell polynomials and complete r-extended Lah–Bell polynomials respectively as multivariate versions of r-Lah numbers and the r-extended Lah–Bell numbers and to investigate some properties and identities for these polynomials. From these investigations we obtain some expressions for the r-Lah numbers and the r-extended Lah–Bell numbers as finite sums.

Bell numbers, determinants and series

2013 ◽  
Vol 123 (2) ◽  
pp. 151-166 ◽  
Author(s):  
P K SAIKIA ◽  
DEEPAK SUBEDI
Keyword(s):  
Bell Numbers

Some inequalities for the Bell numbers

2017 ◽  
Vol 127 (4) ◽  
pp. 551-564 ◽  
Author(s):  
Feng Qi
Keyword(s):  
Bell Numbers

Stirling and Bell Numbers

2020 ◽  
pp. 277-300
Author(s):  
Craig P. Bauer
Keyword(s):  
Bell Numbers

Compositions of a numerical semigroup

2019 ◽  
Vol 29 (5) ◽  
pp. 345-350
Author(s):  
Ze Gu
Keyword(s):  
Nonnegative Integer ◽  
Numerical Semigroup ◽  
Apéry Set ◽  
Wilf’S Conjecture

Abstract Given a numerical semigroup S, a nonnegative integer a and m ∈ S ∖ {0}, we introduce the set C(S, a, m) = {s + aw(s mod m) | s ∈ S}, where {w(0), w(1), ⋯, w(m – 1)} is the Apéry set of m in S. In this paper we characterize the pairs (a, m) such that C(S, a, m) is a numerical semigroup. We study the principal invariants of C(S, a, m) which are given explicitly in terms of invariants of S. We also characterize the compositions C(S, a, m) that are symmetric, pseudo-symmetric and almost symmetric. Finally, a result about compliance to Wilf’s conjecture of C(S, a, m) is given.

Bell–Sheffer exponential polynomials of the second kind

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Pierpaolo Natalini ◽  
Paolo Emilio Ricci
Keyword(s):  
Higher Order ◽  
Bell Numbers ◽  
Integer Sequences ◽  
Exponential Polynomials ◽  
Sheffer Polynomials

AbstractIn recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers and several integer sequences related to them have been studied. In the present paper, new sets of Bell–Sheffer polynomials are introduced. Connections with Bell numbers are shown.

scholarly journals Near-misses in Wilf’s conjecture

2018 ◽  
Vol 98 (2) ◽  
pp. 285-298
Author(s):  
Shalom Eliahou ◽  
Jean Fromentin
Keyword(s):  
Near Misses ◽  
Wilf’S Conjecture

Bell Numbers and Variant Sequences Derived from a General Functional Differential Equation

Integers ◽  
2009 ◽  
Vol 9 (5) ◽  
Author(s):  
H. W. Gould ◽  
Jocelyn Quaintance
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Bell Numbers ◽  
Functional Differential

AbstractIt is well known that the Bell numbers

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