Finitely continuous differentials on generalized power series

Year, pages: 2014, 267 - 280

Let $κ[[\e^\mathcal{G}]]$ be the field of generalized power series with exponents in a totally ordered Abelian group $\mathcal{G}$ and coefficients in a field $κ$. Given a subgroup $\mathcal{H}$ of $\mathcal{G}$ such that $\mathcal{G}/\mathcal{H}$ is finitely generated, we construct a vector space $Ω_{\mathcal{G}/\mathcal{H}}$ of differentials as a universal object in certain category of $κ[[\e^\mathcal{H}]]$-derivations on $κ[[\e^\mathcal{G}]]$. The vector space $Ω_{\mathcal{G}/\mathcal{H}}$ together with logarithmic residues gives rise to a framework for certain combinatorial phenomena, including the inversion formula for diagonal delta sets.

Huang, I. 2014. Finitely continuous differentials on generalized power series. In Mathematica Slovaca, vol. 64, no.2, pp. 267-280. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0201-2

Huang, I. (2014). Finitely continuous differentials on generalized power series. Mathematica Slovaca, 64(2), 267-280. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0201-2