1,3

Note: the number of fixed terms in each successive range [0,n!-1] is given by A000045[n+1] (Fibonacci numbers) and the corresponding positions by A060112. (Foata transform fixes a permutation only if it is composed of disjoint adjacent transpositions)

FoataPermutationCycleCounts_Lengths_and_LCM := proc(upto_n) local u, n, a, b, i, f; a := []; b := []; f := 1; for i from 0 to upto_n! -1 do b := [op(b), 1+PermRank3R(Foata(PermUnrank3R(i)))]; if((f - 1) = i) then a := [op(a), [CountCycles(b), CycleLengths1(b), CyclesLCM(b)]]; print (a); f := f*(nops(a)+1); fi; od; RETURN(a); end;

lcmlist := proc(a) local z, e; z := 1; for e in a do z := ilcm(z, e); od; RETURN(z); end;

CyclesLCM := b -> lcmlist(map(nops, convert(b, 'disjcyc')));

A065161, A065162. For the requisite Maple procedures see sequences A057502, A057542, A060117, A060125.

Sequence in context: A054092 A096648 A019056 this_sequence A057124 A038237 A069738

Adjacent sequences: A065160 A065161 A065162 this_sequence A065164 A065165 A065166

nonn,more

Antti Karttunen Oct 19 2001