Geodesic
Some congruences for the partial Bell polynomials
Journal of integer sequences, Tome 12 (2009) no. 4.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $B_{n,k}$ and $A_{n}=\sum_{j=1}^{n}B_{n,j}$ with $A_0=1$ be, respectively, the $(n,k)^{\rm th}$ partial and the $n^{\rm th}$ complete Bell polynomials with indeterminate arguments $x_1,x_2,\ldots$. Congruences for $A_{n}$ and $B_{n,k}$ with respect to a prime number have been studied by several authors. In the present paper, we propose some results involving congruences for $B_{n,k}$ when the arguments are integers. We give a relation between Bell polynomials and we apply it to several congruences. The obtained congruences are connected to binomial coefficients.
Classification : 05A10, 11B73, 11B75, 11P83
Keywords: Bell polynomials, congruences, Stirling numbers, binomial coefficients 
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     author = {Mihoubi, Miloud},
     title = {Some congruences for the partial {Bell} polynomials},
     journal = {Journal of integer sequences},
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     number = {4},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_4_a0/}
}
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Mihoubi, Miloud. Some congruences for the partial Bell polynomials. Journal of integer sequences, Tome 12 (2009) no. 4. http://geodesic.mathdoc.fr/item/JIS_2009__12_4_a0/