A065163 - OEIS

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A065163

Maximal orbit size in the symmetric group partitioned by the Foata transform (i.e. a(n) is the max. cycle length found in the corresponding permutations A065181-A065184 in range [0,n!-1]).

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	OFFSET	`1,3`
	COMMENTS	`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)`
	MAPLE	`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')));`
	CROSSREFS	`A065161, A065162. For the requisite Maple procedures see sequences A057502, A057542, A060117, A060125.` `Sequence in context: A096648 A156100 A019056 * A057124 A038237 A148740` `Adjacent sequences: A065160 A065161 A065162 * A065164 A065165 A065166`
	KEYWORD	`nonn,more`
	AUTHOR	`Antti Karttunen Oct 19 2001`

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Last modified February 15 23:34 EST 2012. Contains 205860 sequences.