Comptes Rendus
Combinatorics
Note on some restricted Stirling numbers of the second kind
[Note sur des restrictions des nombres de Stirling de deuxième espèce]
Comptes Rendus. Mathématique, Volume 354 (2016) no. 3, pp. 231-234.

Le but de ce travail est d'établir quelques propriétés des coefficients des polynômes chromatiques de certains graphes. Nous donnons une application sur une restriction des nombres de Stirling de deuxième espèce.

The aim of this work is to establish some properties of the coefficients of the chromatic polynomials of special graphs. An application on (restricted) Stirling numbers of the second kind is considered.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.12.003
Mohammed Said Maamra 1 ; Miloud Mihoubi 1

1 RECITS Laboratory, Faculty of Mathematics, USTHB, P.O. Box 32, El Alia 16111, Bab-Ezzouar, Algiers, Algeria
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Mohammed Said Maamra; Miloud Mihoubi. Note on some restricted Stirling numbers of the second kind. Comptes Rendus. Mathématique, Volume 354 (2016) no. 3, pp. 231-234. doi : 10.1016/j.crma.2015.12.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.12.003/

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

[2] F.M. Dong; K.M. Koh; K.L. Teo Chromatic Polynomials and Chromaticity of Graphs, World Scientific, British Library, 2005

[3] B. Duncan; R. Peele Bell and Stirling numbers for graphs, J. Integer Seq., Volume 12 (2009)

[4] G.H. Hardy; J.E. Littlewood; G. Plóya Inequalities, The University Press, Cambridge, 1952

[5] S. Karlin Total Positivity, vol. I, Stanford University Press, Stanford, 1968

[6] D.C. Kurtz A note on concavity properties of triangular arrays of numbers, J. Comb. Theory, Ser. A, Volume 3 (1972), pp. 135-139

[7] L.L. Liu; Y. Wang On the log-convexity of combinatorial sequences, Adv. Appl. Math., Volume 39 (2007), pp. 453-476

[8] M.S. Maamra; M. Mihoubi The (r1,,rp)-Bell polynomials, Integers, Volume 14 (2014)

[9] M. Mihoubi; M.S. Maamra The (r1,,rp)-Stirling numbers of the second kind, Integers, Volume 12 (2012)

[10] B.E. Sagan Log concave sequences of symmetric functions and analogs of the Jacobi–Trudi determinants, Trans. Amer. Math. Soc., Volume 329 (1992), pp. 795-811

[11] B.E. Sagan Inductive proofs of q-log concavity, Discrete Math., Volume 99 (1992), pp. 298-306

[12] Y. Wang; Y.-N. Yeh Polynomials with real zeros and Pólya frequency sequences, J. Comb. Theory, Ser. A, Volume 109 (2005), pp. 63-74

[13] F.Z. Zhao On log-concavity of a class of generalized Stirling numbers, Electron. J. Comb., Volume 19 (2012)

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