Planar Binomial Coefficients

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dc.creatorGerritzen, Lothar
dc.date2005-02-17
dc.date.accessioned2026-07-07T05:17:07Z
dc.date.available2026-07-07T05:17:07Z
dc.descriptionThe notion of binomial coefficients $T \choose S$ of finite planar, reduced rooted trees $T, S$ is defined and a recursive formula for its computation is shown. The nonassociative binomial formula $$(1 + x)^T = \displaystyle \sum_S {T \choose S} x^S$$ for powers relative to $T$ is derived. Similarly binomial coefficients $ T \choose S, V$ of the second kind are introduced and it is shown that $(x \otimes 1 + 1 \otimes x)^T= \displaystyle \sum_{S, V} {T \choose S, V} (x^S \otimes x^V)$ The roots $\sqrt[T]{1+x}= (1 + x) ^{T^{-1}}$ which are planar power series $f$ such that $ f^T= 1+x$ are considered. Formulas for their coefficients are given.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0502380
dc.identifierhttp://arxiv.org/abs/math/0502380
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74234
dc.subjectRings and Algebras
dc.subject17A50
dc.titlePlanar Binomial Coefficients
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