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.
Accepté le :
Publié le :
@article{CRMATH_2021__359_1_57_0, author = {Mihoubi, Miloud and Taharbouchet, Said}, 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}, language = {en}, url = {http://www.numdam.org/articles/10.5802/crmath.147/} }
TY - JOUR AU - Mihoubi, Miloud AU - Taharbouchet, Said 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 UR - http://www.numdam.org/articles/10.5802/crmath.147/ DO - 10.5802/crmath.147 LA - en ID - CRMATH_2021__359_1_57_0 ER -
%0 Journal Article %A Mihoubi, Miloud %A Taharbouchet, Said %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 %U http://www.numdam.org/articles/10.5802/crmath.147/ %R 10.5802/crmath.147 %G en %F CRMATH_2021__359_1_57_0
Mihoubi, Miloud; Taharbouchet, Said. Polynomials with real zeros via special polynomials. Comptes Rendus. Mathématique, Tome 359 (2021) no. 1, pp. 57-64. doi : 10.5802/crmath.147. http://www.numdam.org/articles/10.5802/crmath.147/
[1] Curious congruences related to the Bell polynomials, Quaest. Math., Volume 41 (2018) no. 3, pp. 437-448 | DOI | MR | Zbl
[2] Real-rooted polynomials via generalized Bell umbra, Notes Number Theory Discrete Math., Volume 25 (2019) no. 2, pp. 136-144 | DOI
[3] Real zeros and partitions without singleton blocks, Eur. J. Comb., Volume 51 (2016), pp. 500-510 | DOI | MR | Zbl
[4] 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] Advanced Combinatorics.The art of finite and infinite expansions, Reidel Publishing Company, 1974 (Translated from the french by J.W. Nienhuys) | Zbl
[6] Chromatic polynomials and chromaticity of graphs, World Scientific, 2005 | Zbl
[7] Applications of the classical umbral calculus, Algebra Univers., Volume 49 (2003) no. 4, pp. 397-434 | DOI | MR | Zbl
[8] The -Bell polynomials, Integers, Volume 14 (2014), A34, 14 pages | Zbl
[9] Bell polynomials and binomial type sequences, Discrete Math., Volume 308 (2008) no. 12, pp. 2450-2459 | DOI | MR | Zbl
[10] The -Stirling numbers of the second kind, Integers, Volume 12 (2012) no. 5, A35, pp. 1047-1059 | Zbl
[11] Some identities involving Appell polynomials, Quaest. Math., Volume 43 (2019) no. 2, pp. 203-212 | DOI | MR
[12] The Umbral Calculus, Pure and Applied Mathematics, 111, Academic Press Inc., 1984 | MR | Zbl
[13] 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] Polynomials with real zeros and Pólya frequency sequences, J. Comb. Theory, Volume 109 (2005) no. 1, pp. 63-74 | DOI | Zbl
Cité par Sources :