Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ arXiv.org e-Print Ar...arrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
arXiv.org e-Print Archive
Preprint . 2024
Data sources: arXiv.org e-Print Archive
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 2024
Data sources: zbMATH Open
Utilitas Mathematica
Article . 2024 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2024
License: CC BY
Data sources: Datacite
 View all 4 versions
Claim

This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

Convolution Identities of Stirling Numbers

Convolution identities of Stirling numbers
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 31 Dec 2024Embargo end date: 01 Jan 2024Publisher:Combinatorial PressJournal:Utilitas Mathematica, volume 121, pages 3-9 (issn: 0315-3681, Copyright policy )
Authors: Li, Nadia N.; Chu, Wenchang;

doi: 10.61091/um121-01 , 10.48550/arxiv.2404.09891

arXiv: 2404.09891

Convolution Identities of Stirling Numbers

Abstract

By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial identities (Theorems 3.1 and 3.3) are established as applications, that contain some well–known convolution formulae on Stirling numbers as special cases.

Related Organizations
Keywords

convolution formula, generating function, 05A10, 11B65, recurrence relation, Exact enumeration problems, generating functions, Stirling number of the first kind, FOS: Mathematics, Bell and Stirling numbers, Mathematics - Combinatorics, Combinatorics (math.CO), Factorials, binomial coefficients, combinatorial functions, Stirling number of the second kind

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green