9. Stallings foldings

9.1 Some theory

9.2 Foldings

A finitely generated subgroup of a finitely generated free group is given through a list whose first element is the number of generators of the free group and the remaining elements are the generators of the subgroup.

A generator of the subgroup may be given through a string of letters or through a list of positive integers as decribed in what follows.

When the free group has n generators, the n+j^th letter of the alphabet should be used to represent the formal inverse of the j^th generator which is represented by the j^th letter. The number of generators of the free group must not exceed 7.

For example, [2,"abc","bbabcd"] means the subgroup of the free group on 2 generators generated by aba^-1 and bbaba^-1b^-1. The same subgroup may be given as [2,[1,2,3],[2,2,1,2,3,4]]

9.2-1 FlowerAutomaton
> FlowerAutomaton( L )( function )

The argument L is a subgroup of the free group given through any of the representations described above.

9.2-2 FoldFlowerAutomaton
> FoldFlowerAutomaton( A )( function )

Makes identifications on the flower automaton A




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