Geodesic
On binomial identities in arbitrary bases
Journal of integer sequences, Tome 19 (2016) no. 5
We first extend the digital binomial identity as given by Nguyen et al. to an identity in an arbitrary base $b$, by introducing the $b$-ary binomial coefficients. Then, we study the properties of these coefficients such as their orthogonality, their link with Lucas theorem and their extension to multinomial coefficients. Finally, we analyze the structure of the corresponding $b$-ary Pascal-like triangles.
Classification : 05C30, 05C78
Keywords: b-ary expansion, b-ary binomial coefficient, Lucas theorem 
@article{JIS_2016__19_5_a5,
     author = {Jiu,  Lin and Vignat,  Christophe},
     title = {On binomial identities in arbitrary bases},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {5},
     zbl = {1342.05068},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_5_a5/}
}
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Jiu,  Lin; Vignat,  Christophe. On binomial identities in arbitrary bases. Journal of integer sequences, Tome 19 (2016) no. 5. http://geodesic.mathdoc.fr/item/JIS_2016__19_5_a5/