Re: Partition strangeness

From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 01/11/05 

Date: Tue, 11 Jan 2005 11:45:45 +0000

Hauke Reddmann wrote:

> Robin Chapman <rjc@ivorynospamtower.freeserve.co.uk> wrote:
>> Hauke Reddmann wrote:
>
>>> Now define the "jaggedness" J of a tableaux to be the
>>> difference between the longest and shortest row.
>>> (In the above, 0 3 1 2 1 1 0.)
>
>> What actually are you asking?
>
> a) Why do exactly n partitions of n of jaggedness <=1
> exist? (Clean formulation of the handwave proof.)

That's easy. Look at the conjugate partition. A partition
mu has jaggedness <= 1 iff its conjugate mu* has all parts,
save perhaps the smallest, equal. That is if mu* has largest
part k it has [n/k] parts equal to k, and perhaps an extra
part equal to n - [n/k]k (unless this is zero). So these mu*
are parametrized by k where 1 <= k <= n. 

-- 
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9"
Francis Wheen, _How Mumbo-Jumbo Conquered the World_