Combinatorics/Number theory
A note on the r-Whitney numbers of Dowling lattices
Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 649-655.

The complete and elementary symmetric functions are specializations of Schur functions. In this paper, we use this fact to give two identities for the complete and elementary symmetric functions. This result can be used to proving and discovering some algebraic identities involving r-Whitney and other special numbers.

Les fonctions symétriques complètes et élémentaires sont des spécialisations de fonctions de Schur. Dans cet article, nous utilisons ce fait pour donner deux identités pour les fonctions symétriques complètes et élémentaires. Ce résultat peut être utilisé pour démontrer et découvrir des identités algébriques impliquant les nombres r-Whitney et dʼautres nombres spéciaux.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.09.011
Merca, Mircea 1

1 Department of Mathematics, University of Craiova, 200585 Craiova, Romania
@article{CRMATH_2013__351_17-18_649_0,
     author = {Merca, Mircea},
     title = {A note on the {\protect\emph{r}-Whitney} numbers of {Dowling} lattices},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {649--655},
     publisher = {Elsevier},
     volume = {351},
     number = {17-18},
     year = {2013},
     doi = {10.1016/j.crma.2013.09.011},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2013.09.011/}
}
TY  - JOUR
AU  - Merca, Mircea
TI  - A note on the r-Whitney numbers of Dowling lattices
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 649
EP  - 655
VL  - 351
IS  - 17-18
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2013.09.011/
DO  - 10.1016/j.crma.2013.09.011
LA  - en
ID  - CRMATH_2013__351_17-18_649_0
ER  - 
%0 Journal Article
%A Merca, Mircea
%T A note on the r-Whitney numbers of Dowling lattices
%J Comptes Rendus. Mathématique
%D 2013
%P 649-655
%V 351
%N 17-18
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2013.09.011/
%R 10.1016/j.crma.2013.09.011
%G en
%F CRMATH_2013__351_17-18_649_0
Merca, Mircea. A note on the r-Whitney numbers of Dowling lattices. Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 649-655. doi : 10.1016/j.crma.2013.09.011. http://www.numdam.org/articles/10.1016/j.crma.2013.09.011/

[1] Andrews, G.E. The Theory of Partitions, Addison–Wesley Publishing, 1976

[2] Andrews, G.E.; Gawronski, W.; Littlejohn, L.L. The Legendre–Stirling numbers, Discrete Math., Volume 311 (2011), pp. 1255-1272

[3] Andrews, G.E.; Littlejohn, L.L. A combinatorial interpretation of the Legendre–Stirling numbers, Proc. Amer. Math. Soc., Volume 137 (2009) no. 8, pp. 2581-2590

[4] Benoumhani, M. On Whitney numbers of Dowling lattices, Discrete Math., Volume 159 (1996), pp. 13-33

[5] Benoumhani, M. On some numbers related to Whitney numbers of Dowling lattices, Adv. Appl. Math., Volume 19 (1997), pp. 106-116

[6] Benoumhani, M. Log-concavity of Whitney numbers of Dowling lattices, Adv. Appl. Math., Volume 22 (1999), pp. 186-189

[7] Broder, A.Z. The r-Stirling numbers, Discrete Math., Volume 49 (1984), pp. 241-259

[8] Call, G.S.; Velleman, D.J. Pascalʼs matrices, Am. Math. Mon., Volume 100 (1993) no. 4, pp. 372-376

[9] Cheon, G.-S.; Jung, J.-H. r-Whitney numbers of Dowling lattices, Discrete Math., Volume 312 (2012), pp. 2337-2348

[10] Davey, B.A.; Priestley, H.A. Introduction to Lattices and Order, Cambridge University Press, 2002

[11] Dowling, T.A. A class of geometric lattices based on finite groups, J. Comb. Theory, Ser. B, Volume 14 (1973), pp. 61-86

[12] Everitt, W.N.; Littlejohn, L.L.; Wellman, R. Legendre polynomials, Legendre–Stirling numbers, and the left-definite analysis of the Legendre differential expression, J. Comput. Appl. Math., Volume 148 (2002) no. 1, pp. 213-238

[13] Gelineau, Y.; Zeng, J. Combinatorial interpretations of the Jacobi–Stirling numbers, Electron. J. Comb., Volume 17 (2010), p. R70

[14] Macdonald, I.G. Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford, 1995

[15] Merca, M. A convolution for the complete and elementary symmetric functions, Aequ. Math. (2012) | DOI

[16] Mező, I. On the maximum of r-Stirling numbers, Adv. Appl. Math., Volume 41 (2008) no. 3, pp. 293-306

[17] Mező, I. New properties of r-Stirling series, Acta Math. Hung., Volume 119 (2008), pp. 341-358

[18] Mező, I. A new formula for the Bernoulli polynomials, Results Math., Volume 58 (2010), pp. 329-335

[19] Mongelli, P. Combinatorial interpretations of particular evaluations of complete and elementary symmetric functions, Electron. J. Comb., Volume 19 (2012) no. 1 (#P60)

[20] Riordan, J. Combinatorial Identities, John Wiley & Sons, New York, 1968

Cited by Sources: