A057542 Maximum cycle length in each permutation between A038776(1) and A038776(A000108(n)).

1, 1, 1, 3, 4, 16, 87, 202, 607, 1441, 4708, 41888, 44741, 339108, 1617551

Offset: 0

Author

Antti Karttunen, Sep 07 2000

Keywords

• nonn
• more

Links

• Sean A. Irvine, Java program (github)

Crossrefs

Cycle lengths of permutation A038776 given in A038774.

Cf. A057543, A057544, A057545.

LCM's of all cycles: A060113.

Programs

Maple

map(lmax,Bf2DfBinTreePermutationCycleLengths(some_value)); (e.g. 10)
bf2df := s -> (btbf2df(binrev(s),0,1)/2); # btbf2df and binrev given in A038776
Bf2DfBinTreePermutationCycleLengths := proc(upto_n) local u,n,a,r,b; a := []; for n from 0 to upto_n do b := []; u := (binomial(2*n,n)/(n+1)); for r from 0 to u-1 do b := [op(b),1+CatalanRank(n,bf2df(CatalanUnrank(n,r)))]; od; a := [op(a),CycleLengths1(b)]; od; RETURN(a); end;
CycleLengths1 := b -> [[(nops(b)-convert(map(nops,convert(b,'disjcyc')),`+`)),`*`,1],op(map(nops,convert(b,'disjcyc')))];
last_term := proc(l) local n: n := nops(l); if(0 = n) then ([]) else (op(n,l)): fi: end:
lmax := proc(a) local e,z; z := 0; for e in a do if whattype(e) = list then e := last_term(e); fi; if e > z then z := e; fi; od; RETURN(z); end;

Extensions

a(11)-a(14) from Sean A. Irvine, Jun 13 2022