Sur le groupe d'interpolation

Details Sur le groupe d'interpolation Sur le groupe d'interpolation

2006-09-26

arxiv.org/abs/math/0609736v3

Mathematics

Combinatorics

40 pages, in french, some improvements and new chapter on "Riordan matrices" added

Scientific paper

We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix exponential between its Lie algebra and its matrix representation gives rise to a function with interesting properties extending the usual exponential function to two variables (which are formal power series) We finish with an application to enumerative combinatorics and the description of an algebra which generalizes the interpolation group.

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