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Generalized Stirling and Lah numbers

Carl G. Wagner
1996 Discrete Mathematics  
Within this theory three generalizations of Stifling numbers of the second kind, and of Lah numbers, are developed.  ...  The theory of modular binomial lattices enables the simultaneous combinatorial analysis of finite sets, vector spaces, and chains.  ...  Acknowledgements I am grateful to Reid Davis for assistance in the formulation and proof of Theorem 5.1.  ... 
doi:10.1016/0012-365x(95)00112-a fatcat:wpsntlgbcvddzlzkftaplug36m

Some Theorems on Tauber's Generalized Stirling, Lah and Bell Numbers

Roberto Bagsarsa Corcino, Cristina Bordaje Corcino, Gladys Jane Rama
2019 European Journal of Pure and Applied Mathematics  
In this paper, some properties for Tauber's generalized Stirling and Lah numbers are obtained including other forms of recurrence relations, orthogonality and inverse relations, rational generating function  ...  and explicit formual in symmetric function form.  ...  The Bell numbers B h,n can be computed in terms of Tauber's generalized Lah and Stirling numbers of the second kind.  ... 
doi:10.29020/nybg.ejpam.v12i3.3424 fatcat:3x4h6g5iuzbp3fg6x5grxg545i

On xD-Generalizations of Stirling Numbers and Lah Numbers via Graphs and Rooks [article]

Sen-Peng Eu, Tung-Shan Fu, Yu-Chang Liang, Tsai-Lien Wong
2017 arXiv   pre-print
Interestingly, the coefficients in individual expansions turn out to be generalizations of the Stirling numbers of the first kind and the Lah numbers.  ...  This paper studies the generalizations of the Stirling numbers of both kinds and the Lah numbers in association with the normal order problem in the Weyl algebra W=〈 x,D|Dx-xD=1〉.  ...  Stirling numbers of the first kind and Lah numbers for words.  ... 
arXiv:1701.00600v1 fatcat:5lvjgwlfbffe7mkovxmgw2kco4

On xD-Generalizations of Stirling Numbers and Lah Numbers via Graphs and Rooks

Sen-Peng Eu, Tung-Shan Fu, Yu-Chang Liang, Tsai-Lien Wong
2017 unpublished
Interestingly, the coefficients in individual expansions turn out to be generalizations of the Stirling numbers of the first kind and the Lah numbers.  ...  This paper studies the generalizations of the Stirling numbers of both kinds and the Lah numbers in association with the normal ordering problem in the Weyl algebra W = x, D|Dx − xD = 1.  ...  Introduction The Stirling numbers of both kinds and the Lah numbers are ubiquitous in combinatorics.  ... 
fatcat:teylshf23jc67jk2fqj77c26ua

EVOLUTIONARY MATHEMATICS AND SCIENCE FOR ULTIMATE GENERALIZATION OF LAH NUMBERS/(BINOMIAL COEFFICIENTS): SUMS/(ALTERNATE SUMS) OF ORTHOGONAL PRODUCTS OF STIRLING NUMBERS [chapter]

Hung-ping Tsao, Lawrence K Wang
2021
Evolutionary mathematics and science for Ultimate Generalization of Lah Numbers/(Binomial Coefficients): Sums/(Alternate Sums) of Orthogonal Products of Stirling Numbers.  ...  STEAM-VOL3-NUM6-JUN2021; ISBN 978-0-9890870-3-2. ...............ABSTRACT: We first introduce Stirling and Lah numbers via recursion and express Lah numbers and binomial coefficients as sums and alternate  ...  FOR ULTIMATE GENERALIZATION OF LAH NUMBERS/(BINOMIAL COEFFICIENTS): SUMS/(ALTERNATE SUMS) OF ORTHOGONAL PRODUCTS OF STIRLING NUMBERS" is Dr.  ... 
doi:10.17613/xvkz-t375 fatcat:no3fler475chxk5qnwcvfr3m3e

An Explicit Formula for the Bell Numbers in Terms of the Lah and Stirling Numbers

Feng Qi
2015 Mediterranean Journal of Mathematics  
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Lah numbers and Stirling numbers of the second kind.  ...  find a new explicit formula for computing Bell numbers B n in terms of Lah numbers L(n, k) and Stirling numbers of the second kind S(n, k). (10) Proof.  ...  There are two kinds of Stirling numbers: Stirling numbers of the first and second kinds.  ... 
doi:10.1007/s00009-015-0655-7 fatcat:64fy3ptyejgvjnib7zekdxnvle

The r-Bell numbers and matrices containing non-central Stirling and Lah numbers

Roberto B. Corcino, Cristina B. Corcino, Jeneveb T. Malusay, Gaea Iolanthe Mari R. Bercero
2019 Journal of Mathematics and Computer Science  
Moreover, some matrix relations are obtained involving r-Bell numbers, r-Stirling numbers of the second kind, r-Lah numbers, non-central Stirling numbers of the second kind, and the ordinary Lah numbers  ...  The other formula is expressed in terms of the non-central Stirling numbers of the second kind and the ordinary Lah numbers.  ...  The authors would also like to thank the referees for their helpful comments and suggestions.  ... 
doi:10.22436/jmcs.019.03.05 fatcat:d23epglczfdo3gtnhobhqh2x7u

Analogies of the Qi formula for some Dowling type numbers [article]

Roberto B. Corcino, Jeneveb T. Malusay, Joy Antonette Cillar, Gladys Jane Rama, Oscar Vincent Silang, Ianna Marie Tacoloy
2018 arXiv   pre-print
In the paper, the authors establish explicit formulas for the Dowling numbers and their generalizations in terms of generalizations of the Lah numbers and the Stirling numbers of the second kind.  ...  These results gen- eralize the Qi formula for the Bell numbers in terms of the Lah numbers and the Stirling numbers of the second kind.  ...  The authors wish to thank the anonymous referee for reading the manuscript thoroughly which resulted in numerous corrections and improvements.  ... 
arXiv:1808.02663v1 fatcat:q4vutyxxirf2bnrquywvjuwddm

Associated Lah numbers and r-Stirling numbers [article]

Hacene Belbachir, Imad Eddine Bousbaa
2014 arXiv   pre-print
An extension of the associated Stirling and Lah numbers to the r-Stirling and r-Lah numbers are also given.  ...  We introduce the associated Lah numbers. Some recurrence relations and convolution identities are established.  ...  In section 9, we propose some generating functions of the s-associated r-Stirling numbers. The s-associated Lah numbers We start by introducing the s-associated Lah numbers.  ... 
arXiv:1404.5573v2 fatcat:jqyabdubgbfytbnxemh2yrxofa

Page 4059 of Mathematical Reviews Vol. 58, Issue 6 [page]

1979 Mathematical Reviews  
Several variants of the inversion, single and repeated, of linear relations involving generalized Stirling and Lah numbers are con- sidered.  ...  “In this paper we give a systematic description of the basic properties of generalized Stirling and Lah numbers, and derive some new formulas involving these numbers.”  ... 

Inversions relating Stirling, tanh, Lah numbers and an application to Mathematical Statistics [article]

G. Della Riccia
2004 arXiv   pre-print
Inversion formulas have been found, converting between Stirling, tanh and Lah numbers.  ...  New identities for Stirling and tangent numbers and polynomials have been derived from the general inverse relations.  ...  Since in the third and fourth inversion formulas Stirling numbers convert between Lah and tanh numbers, and in the fifth and sixth tanh numbers convert between Lah and Stirling numbers, the proof is complete  ... 
arXiv:math/0405594v1 fatcat:cj667n2d5rczhonjss5ryv4kue

Convolutions for Stirling numbers, Lah numbers, and binomial coefficients [article]

Khristo N. Boyadzhiev
2021 arXiv   pre-print
We present various identities in the form of convolutions involving Stirling numbers of both kinds, Lah numbers, and binomial coefficients. Certain convolution polynomials are discussed also.  ...  In this article we carry out a systematic study of such convolutions for the double sequences of Stirling numbers of the first and second kinds, ( , ) s n k and ( , ) S n k , the Lah numbers ( , ) L n  ...  In this study we produce various identities relating the above numbers. Excellent reference books for the Stirling and Lah numbers are the classical books of Comtet [15] and Graham et al. [17] .  ... 
arXiv:2103.15644v1 fatcat:souhpsoucredtfxidihldkkht4

Multi-Lah numbers and multi-Stirling numbers of the first kind

Dae San Kim, Hye Kyung Kim, Taekyun Kim, Hyunseok Lee, Seongho Park
2021 Advances in Difference Equations  
AbstractIn this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple  ...  In more detail, we represent the multi-Bernoulli numbers in terms of the multi-Stirling numbers of the first kind and vice versa, and the multi-Lah numbers in terms of multi-Stirling numbers.  ...  In more detail, we represent the multi-Bernoulli numbers in terms of the multi-Stirling numbers of the first kind and vice versa, and the multi-Lah numbers in terms of multi-Stirling numbers.  ... 
doi:10.1186/s13662-021-03568-6 fatcat:7eiexb5t65gjlotrh7wo3j7ws4

Lah numbers and Laguerre polynomials of order negative one [article]

Khristo N. Boyadzhiev (Department of Mathematics and Statistics, Ohio Northern University, Ada, OH)
2016 arXiv   pre-print
In this article we point out interesting connections among Lah numbers, Laguerre polynomials of order negative one, and exponential polynomials.  ...  and(1.5). This will reveal interesting connections of Lah numbers to Laguerre polynomials and also to Stirling numbers.  ...  Let ( , ) s n k and ( , ) S n k be the Stirling numbers of the first kind and the second kind correspondingly (see [9] ).  ... 
arXiv:1612.02876v1 fatcat:ssncwpaa5rag5flflknaaw76sq

Recurrences of Stirling and Lah numbers via second kind Bell polynomials

Feng Qi, Pierpaolo Natalini, Paolo Emilio Ricci
2020 Discrete Mathematics Letters  
first and second kinds, for 1-associate Stirling numbers of the second kind, for the Lah numbers, and for the binomial coefficients.  ...  Keywords: recurrence; Bell polynomial of the second kind; Stirling number; 1-associate Stirling number of the second kind; Lah number.  ...  Acknowledgment The authors are thankful to anonymous referees for their careful corrections, helpful suggestions, and valuable comments on the original version of this paper.  ... 
doaj:4cf44b296dd44e88bad93e21fd5e78b1 fatcat:go7lkoh5affznkbkclapbywbrq
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