1 citations · 1 across the 7 of their papers we have counts for
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Ordered groups of formal series, and a conjugacy problem
Vincent Bagayoko
Given an ordered field of formal series over an ordered field equipped with a composition law $\circ \colon \mathbb{T} \times \mathbb{T}^{>\mathbb{R}} \lo…
Taylor expansions over generalised power series
Vincent Bagayoko, Vincenzo Mantova
We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expan…
Hyperseries subfields of surreal numbers
Vincent Bagayoko
We study subfields of surreal numbers, called hyperseries fields, that are suited to be equipped with derivations and composition laws. We show how to define embeddings on hyperser…
Sign sequences of log-atomic numbers
Vincent Bagayoko
Log-atomic numbers are surreal numbers whose iterated logarithms are monomials, and consequently have a trivial expansion as transseries. Presenting surreal numbers as sign sequenc…
On ordered groups of regular growth rates
Vincent Mamoutou Bagayoko
We introduce an elementary class of linearly ordered groups, called growth order groups, encompassing certain groups under composition of formal series (e.g. transseries) as well a…
Surreal numbers as hyperseries
Vincent Bagayoko, Joris van der Hoeven
Surreal numbers form the ultimate extension of the field of real numbers with infinitely large and small quantities and in particular with all ordinal numbers. Hyperseries can be r…