Identities related to integer partitions and complete Bell polynomials
Algebra and discrete mathematics, Tome 24 (2017) no. 1, pp. 158-168.

Voir la notice de l'article dans Math-Net.Ru

Using the (universal) Theorem for the integer partitions and the $q$-binomial Theorem, we give arithmetical and combinatorial identities for the complete Bell polynomials as generating functions for the number of partitions of a given integer into $k$ parts and the number of partitions of $n$ into a given number of parts.
Mots-clés : complete Bell polynomials, integer partitions, $q$-binomial Theorem. 
@article{ADM_2017_24_1_a9,
     author = {Miloud Mihoubi and Hac\`ene Belbachir},
     title = {Identities related to integer partitions and complete {Bell} polynomials},
     journal = {Algebra and discrete mathematics},
     pages = {158--168},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2017},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/ADM_2017_24_1_a9/}
}
TY  - JOUR
AU  - Miloud Mihoubi
AU  - Hacène Belbachir
TI  - Identities related to integer partitions and complete Bell polynomials
JO  - Algebra and discrete mathematics
PY  - 2017
SP  - 158
EP  - 168
VL  - 24
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/ADM_2017_24_1_a9/
LA  - en
ID  - ADM_2017_24_1_a9
ER  - 
%0 Journal Article
%A Miloud Mihoubi
%A Hacène Belbachir
%T Identities related to integer partitions and complete Bell polynomials
%J Algebra and discrete mathematics
%D 2017
%P 158-168
%V 24
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/ADM_2017_24_1_a9/
%G en
%F ADM_2017_24_1_a9
Miloud Mihoubi; Hacène Belbachir. Identities related to integer partitions and complete Bell polynomials. Algebra and discrete mathematics, Tome 24 (2017) no. 1, pp. 158-168. https://geodesic-test.mathdoc.fr/item/ADM_2017_24_1_a9/

[1] G. E. Andrews, The Theory of Partitions, Cambridge, 1998 | MR

[2] G. E. Andrews, K. Eriksson, Integer Partitions, Cambridge, 2004 | MR

[3] A. Altin, E. Erkuş, F. Taşdelen, “The $q$-Lagrange polynomials in several variables”, Taiwanese J. Math., 10:5, September (2006), 1131–1137 | DOI | MR | Zbl

[4] H. Belbachir, “Determining the mode for convolution powers for discrete uniform distribution”, Probab. Engrg. Inform. Sci., 25:4 (2011), 469–475 | DOI | MR | Zbl

[5] H. Belbachir, S. Bouroubi, A. Khelladi, “Connection between ordinary multinomials, generalized Fibonacci numbers, partial Bell partition polynomials and convolution powers of discrete uniform distribution”, Ann. Math. Inform., 35 (2008), 21–30 | MR | Zbl

[6] H. Belbachir, M. Mihoubi, “The (exponential) bipartitional polynomials and polynomial sequences of trinomial type: Part II”, Integers, 11 (2011), A29, 12 | DOI | MR

[7] H. Belbachir, M. Mihoubi, “The (exponential) multipartitional polynomials and polynomial sequences of multinomial type, Part II”, Arab J. Math. Sci., 21:1 (2015), 2–14 | MR | Zbl

[8] E. T. Bell, “Exponential polynomials”, Annals of Math., 35 (1934), 258–277 | DOI | MR

[9] B. C. Berndt, Ramanujan's Notebooks, v. III, Springer-Verlag, New York–Berlin–Heibelberg–Tokyo, 1991 | MR | Zbl

[10] W.-C. C. Chan, C.-J. Chyan, H. M. Srivastava, “The Lagrange polynomials in several variables”, Integral Transform. Spec. Funct., 12 (2001), 139–148 | DOI | MR | Zbl

[11] C. A. Charalambides, Enumerative Combinatorics, Chapman, Boca Raton–London–New York–Washington, D.C.; A CRC Press Company, 2001 | MR

[12] C. B. Collins, “The role of Bell polynomials in integration”, J. Comput. Appl. Math., 131 (2001), 195–222 | DOI | MR | Zbl

[13] L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company, Dordrecht–Boston, 1974 | MR | Zbl

[14] B. Germano, M. R. Martinelli, “Bell polynomials and generalized Blissard problem”, Math. Comput. Modelling, 53 (2011), 964–969 | DOI | MR | Zbl

[15] M. Mihoubi, “Partial Bell polynomials and inverse relations”, J. Integer Seq., 13 (2010), 10.4.5 | MR | Zbl

[16] M. Mihoubi, “Bell polynomials and binomial type sequences”, Discrete Math., 308 (2008), 2450–2459 | DOI | MR | Zbl

[17] M. Mihoubi, “The role of binomial type sequences in determination identities for Bell polynomials”, Ars Combinatoria, 111:2013, 323–337 | MR | Zbl

[18] M. Mihoubi, “Some congruences for the partial Bell polynomials”, J. Integer Seq., 12 (2009), 09.4.1 | MR | Zbl

[19] M. Mihoubi, H. Belbachir, “The (exponential) bipartitional polynomials and polynomial sequences of trinomial type: Part I”, Integers, 11 (2011), A18, 17 | DOI | MR

[20] M. Mihoubi, H. Belbachir, “The (exponential) multipartitional polynomials and polynomial sequences of multinomial type, Part I”, Arab J. Math. Sci., 20:2 (2014), 233–245 | MR | Zbl