no. 3
Combinatorics
Note on some restricted Stirling numbers of the second kind
[Note sur des restrictions des nombres de Stirling de deuxième espèce]

Présenté par : the Editorial Board

Maamra, Mohammed Said1 ; Mihoubi, Miloud1
1 RECITS Laboratory, Faculty of Mathematics, USTHB, P.O. Box 32, El Alia 16111, Bab-Ezzouar, Algiers, Algeria
Comptes Rendus. Mathématique, Tome 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
Maamra, Mohammed Said 1 ; Mihoubi, Miloud 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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