[r-t] Gangnam (or whatever) etc.

Simon Gay Simon.Gay at glasgow.ac.uk
Wed May 14 11:36:15 UTC 2014

Yes, I should have made the assumptions clear:

- fixed treble (this is the basis for identifying the lead heads of 
leads that contain rows with the treble in 6th place)

- no half lead singles (this is the basis for saying that within a given 
lead, all of the rows with the treble in 6th place have the same parity).

Richard has already given a composition with variable treble.

I imagine that it might be possible to use, let's say, a 3456 half lead 
single, and produce 30 leads, each containing a half lead single, which 
between them contain all 720 changes. Then maybe it would be possible to 
insert these 30 leads into a 6-extent block, and produce a 5040.


On 14/05/2014 12:13, Don Morrison wrote:
> On Wed, May 14, 2014 at 6:51 AM, Simon Gay <Simon.Gay at glasgow.ac.uk> wrote:
>> Consider the rows of the form 56xxx1 and 65xxx1.
>> There are 12 such rows, and they occur 4 per lead, with lead heads
>> of the form 15xxx6 or 16xxx5.
>> In a multi-extent block in which each row occurs n times, we
>> therefore have 3n leads which between them contain all the
>> occurrences of 56xxx1 and 65xxx1.
>> Within one such lead, all occurrences of 56xxx1 or 65xxx1 have the
>> same parity. Therefore half of these leads need to have positive
>> lead heads, and the other half need to have negative lead heads.
> This argument only applies in the absence of half-lead singles, right?
> Can it be extended to one counting suitable rows in a half-lead, from
> lead heads and lead ends, with some suitable constraint on how those
> lead heads and lead ends match up or something?

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