7.48 EulerianFunction

EulerianFunction( G, n )

EulerianFunction returns the number of n-tuples (g_1, g_2, ldots g_n) of elements of the group G that generate the whole group G. The elements of a tuple need not be different.

    gap> s4 := SymmetricGroup( AgWords, 4 );;
    gap> ss4 := SpecialAgGroup( s4 );;
    gap> EulerianFunction( ss4, 1 );
    0
    gap> EulerianFunction( ss4, 2 );
    216
    gap> EulerianFunction( ss4, 3 );
    10080 

Currently EulerianFunction can only be applied to special Ag groups (see Special Ag Groups).

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