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Comptes Rendus. Mathématique
Théorie des fonctions
Polynomials with real zeros via special polynomials
[Polynômes à racines réelles via des polynômes spéciaux]
Comptes Rendus. Mathématique, Tome 359 (2021) no. 1, pp. 57-64.

Dans ce papier, nous utilisons des polynômes particuliers pour établir quelques résultats sur les polynômes à racines réelles. Les polynômes considérés sont des polynômes de Bell et des polynômes de Hermite.

In this paper, we use particular polynomials to establish some results on the real rootedness of polynomials. The considered polynomials are Bell polynomials and Hermite polynomials.

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DOI : https://doi.org/10.5802/crmath.147
Miloud Mihoubi 1 ; Said Taharbouchet 2

1. RECITS Laboratory, Faculty of Mathematics, USTHB, P.O. Box 32, El Alia 16111, Bab-Ezzouar, Algiers, Algeria
2. RECITS Laboratory, Faculty of Mathematics, USTHB, Po Box 32, El Alia 16111, Bab-Ezzouar, Algiers, Algeria
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     author = {Miloud Mihoubi and Said Taharbouchet},
     title = {Polynomials with real zeros via special polynomials},
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Miloud Mihoubi; Said Taharbouchet. Polynomials with real zeros via special polynomials. Comptes Rendus. Mathématique, Tome 359 (2021) no. 1, pp. 57-64. doi : 10.5802/crmath.147. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.147/

[1] Abdelkader Benyattou; Miloud Mihoubi Curious congruences related to the Bell polynomials, Quaest. Math., Volume 41 (2018) no. 3, pp. 437-448 | Article | MR 3799218 | Zbl 1415.11042

[2] Abdelkader Benyattou; Miloud Mihoubi Real-rooted polynomials via generalized Bell umbra, Notes Number Theory Discrete Math., Volume 25 (2019) no. 2, pp. 136-144 | Article

[3] Miklós Bóna; István Mező Real zeros and partitions without singleton blocks, Eur. J. Comb., Volume 51 (2016), pp. 500-510 | Article | MR 3398875 | Zbl 1321.05014

[4] Francesco Brenti Log-concave and unimodal sequences in algebra, combinatorics, and geometry: an update, Jerusalem combinatorics ’93: an international conference in combinatorics, May 9-17, 1993, Jerusalem, Israel (Contemporary Mathematics), Volume 178, American Mathematical Society, 1994, pp. 71-89 | Article | MR 1310575 | Zbl 0813.05007

[5] Louis Comtet Advanced Combinatorics.The art of finite and infinite expansions, Reidel Publishing Company, 1974 (Translated from the french by J.W. Nienhuys) | Zbl 0853.05001

[6] Fengming Dong; Koh Khee Meng; Kee Leong Teo Chromatic polynomials and chromaticity of graphs, World Scientific, 2005 | Zbl 1070.05038

[7] Ira M. Gessel Applications of the classical umbral calculus, Algebra Univers., Volume 49 (2003) no. 4, pp. 397-434 | Article | MR 2022347 | Zbl 1092. 05005

[8] Mohammed S. Maamra; Miloud Mihoubi The (r 1 ,...,r p )-Bell polynomials, Integers, Volume 14 (2014), A34, 14 pages | Zbl 1308.11027

[9] Miloud Mihoubi Bell polynomials and binomial type sequences, Discrete Math., Volume 308 (2008) no. 12, pp. 2450-2459 | Article | MR 2410451 | Zbl 1147.05006

[10] Miloud Mihoubi; Mohammed S. Maamra The (r 1 ,...,r p )-Stirling numbers of the second kind, Integers, Volume 12 (2012) no. 5, A35, pp. 1047-1059 | Zbl 1310.11031

[11] Miloud Mihoubi; Said Taharbouchet Some identities involving Appell polynomials, Quaest. Math., Volume 43 (2019) no. 2, pp. 203-212 | Article | MR 4066678

[12] Steven Roman The Umbral Calculus, Pure and Applied Mathematics, 111, Academic Press Inc., 1984 | MR 741185 | Zbl 0536.33001

[13] Richard Peter Stanley Log-concave and unimodal sequences in algebra, combinatorics, and geometry, Ann. N.Y. Acad. Sci., Volume 576 (1989), pp. 500-534 | Article | MR 1110850 | Zbl 0792.05008

[14] Yi Wang; Yeong-Nan Yeh Polynomials with real zeros and Pólya frequency sequences, J. Comb. Theory, Volume 109 (2005) no. 1, pp. 63-74 | Article | Zbl 1057.05007

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