The special subgroup of invertible non-commutative rational power series as a metric group

Details The special subgroup of invertible non-commutative rational power series as a metric group The special subgroup of invertible non-commutative rational power series as a metric group

2008-04-07

arxiv.org/abs/0804.1092v2

Mathematics

Combinatorics

41 pages

Scientific paper

We give an easy proof of Sch\"utzenberger's Theorem stating that
non-commutative formal power series are rational if and only if they are
recognisable. A byproduct of this proof is a natural metric on a subgroup of
invertible rational non-commutative power series. We describe a few features of
this metric group.

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