Young tableaux cont

[vdmcc]

for once that I'm *not* longwinded:

partitions of 4 in *exactly* 2 parts:

{3,1} and  {2,2}

the first corresponds to a  *set* of Young Tableaux :

Tableaux[{3,1}]
{
{{1,3,4},{2}},
{{1,2,4},{3}},
{{1,2,3},{4}}
}

NumberOfTableaux[{3,1}] is 3; (hook length formula)
the total number for the partitions of 4 in just 2 parts is
3+2=5
this gives the second entry in the row {1,5,3,1},

wouter.


-----Original Message-----
From: John Conway <conway at math.Princeton.EDU>
To: N. J. A. Sloane <njas at research.att.com>
Cc: seqfan at ext.jussieu.fr <seqfan at ext.jussieu.fr>
Date: Wednesday, May 12, 1999 3:15 PM
Subject: Re: Young tableaux cont


>
>
>On Wed, 12 May 1999, N. J. A. Sloane wrote:
>
>> yes, i'm very interested, and i added this entry to the database
>>
>> %I A047884
>> %S A047884
1,1,1,1,2,1,1,5,3,1,1,9,11,4,1,1,19,31,19,5,1,1,34,92,69,29,6,1,1,
>> %T A047884
69,253,265,127,41,7,1,1,125,709,929,583,209,55,8,1,1,251,1936,3356,
>> %U A047884
2446,1106,319,71,9,1,1,461,5336,11626,10484,5323,1904,461,89,10,1
>> %N A047884 Triangle of numbers a(n,k) = no. of Young tableaux
corresponding to partiti
>> ons of n into exactly k parts.
>
>   This is an unnecessarily long title (or, if I'm misunderstanding it,
>a misleading one) - it would be better to delete the words
>"Young tableaux corresponding to".
>
>    A similar comment applies to the next one:
>>
>> %I A000085 M1221 N0469
>> %S A000085
1,1,2,4,10,26,76,232,764,2620,9496,35696,140152,568504,2390480,
>> %T A000085 10349536,46206736,211799312,997313824,4809701440,23758664096,
>> %U A000085
119952692896,618884638912,3257843882624,17492190577600,95680443760576
>> %N A000085 Self-inverse permutations on n letters; Young tableaux with n
cells.
>> %F A000085 a(n) = a(n-1) + (n-1)*a(n-2).
>
>     John Conway
>