Polynomials with real zeros via special polynomials

Miloud Mihoubi; Said Taharbouchet

doi:10.5802/crmath.147

Théorie des fonctions

Polynomials with real zeros via special polynomials
[Polynômes à racines réelles via des polynômes spéciaux]

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

Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 57-64.

Résumé
Abstract

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.

Reçu le : 2019-11-03
Accepté le : 2020-11-06
Publié le : 2021-03-01

Zbl

DOI : 10.5802/crmath.147

Affiliations des auteurs :

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

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2021__359_1_57_0,
     author = {Miloud Mihoubi and Said Taharbouchet},
     title = {Polynomials with real zeros via special polynomials},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {57--64},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {1},
     year = {2021},
     doi = {10.5802/crmath.147},
     zbl = {1443.05019},
     language = {en},
}

TY  - JOUR
AU  - Miloud Mihoubi
AU  - Said Taharbouchet
TI  - Polynomials with real zeros via special polynomials
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 57
EP  - 64
VL  - 359
IS  - 1
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.147
LA  - en
ID  - CRMATH_2021__359_1_57_0
ER  -

%0 Journal Article
%A Miloud Mihoubi
%A Said Taharbouchet
%T Polynomials with real zeros via special polynomials
%J Comptes Rendus. Mathématique
%D 2021
%P 57-64
%V 359
%N 1
%I Académie des sciences, Paris
%R 10.5802/crmath.147
%G en
%F CRMATH_2021__359_1_57_0

Miloud Mihoubi; Said Taharbouchet. Polynomials with real zeros via special polynomials. Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 57-64. doi : 10.5802/crmath.147. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.147/

Bibliographie
Cité par

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

[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 | DOI | Zbl

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

[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 | DOI | MR | Zbl

[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

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

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

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

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

[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

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

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

[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 | DOI | MR | Zbl

[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 | DOI | Zbl

Cité par Sources :

Commentaires - Politique