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Título : | Zeon algebra and combinatorial identities. |
Autor : | Francisco Neto, Antônio Anjos, Petrus Henrique Ribeiro dos |
Palabras clave : | Cauchy integral Grassmann–Berezin integration Faà di Bruno formula Spivey identity Special polynomials |
Fecha de publicación : | 2014 |
Citación : | FRANCISCO NETO, A.; ANJOS, P. H. R. dos. Zeon algebra and combinatorial identities. SIAM Review, v. 56, p. 353-370, 2014. Disponível em: <https://epubs.siam.org/doi/abs/10.1137/130906684?mobileUi=0>. Acesso em: 20 jul. 2017. |
Resumen : | We show that the ordinary derivative of a real analytic function of one variable can be realized as a Grassmann–Berezin-type integration over the Zeon algebra, the Z-integral. As a by-product of this representation, we give new proofs of the Fa`a di Bruno formula and Spivey’s identity [M. Z. Spivey, J. Integer Seq., 11 (2008), 08.2.5], and we recover the representation of the Stirling numbers of the second kind and the Bell numbers of Staples and Schott [European J. Combin., 29 (2008), pp. 1133–1138]. The approach described here is suitable to accommodate new Z-integral representations including Stirling numbers of the first kind, central Delannoy, Euler, Fibonacci, and Genocchi numbers, and the special polynomials of Bell, generalized Bell, Hermite, and Laguerre. |
URI : | http://www.repositorio.ufop.br/handle/123456789/8730 |
metadata.dc.identifier.uri2: | https://epubs.siam.org/doi/abs/10.1137/130906684?mobileUi=0 |
metadata.dc.identifier.doi: | https://doi.org/10.1137/130906684 |
ISSN : | 1095-7200 |
Aparece en las colecciones: | DEPRO - Artigos publicados em periódicos |
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Fichero | Descripción | Tamaño | Formato | |
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ARTIGO_ZeonAlgebraCombinatorial.pdf Restricted Access | 203,78 kB | Adobe PDF | Visualizar/Abrir |
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