[seqfan] Re: bracelets versus Young Tableaux (A000085)

Wouter Meeussen wouter.meeussen at telenet.be
Sun Feb 3 14:08:29 CET 2013


Strong Law of Small Integers again:
the Mathematica 9.0  function "ListNecklaces" is surprisingly slow,
so that a brute force generation (see below)
beats it by a factor of  100 or so. Using that:
Table[Length at bra[2 n - 1], {n, 10}]
{1, 1, 2, 4, 10, 26, 76, 232, 750, 2494}

Table[NumberOfTableaux[n - 1], {n, 10}]
{1, 1, 2, 4, 10, 26, 76, 232, 764, 2620}

't would have been nice though ...

Wouter


-------------- bracelets with n beads, 2 colors, B=W if n even and B=W+1 if 
n odd --------

bra[n_Integer] :=  Union[First[    Sort[Flatten[{#, Reverse /@ #}, 1] &@
    Table[RotateRight[Prepend[#, 0], k], {k, n}]]] & /@
Permutations[Join[0*Range[Floor[n/2-1/2]], 1+0*Range[Floor[n/2]]]]]


-----Original Message----- 
does anybody know of a one-to-one relation between
bracelets of 2n+1 beads with n+1 black ones and n white ones,
and Young Tableaux (or involutions) of the partitions of n? 



More information about the SeqFan mailing list