[r-t] regularity

[Simon J. Gay]

Rephrasing this slightly:

The Plain Bob lead heads are the only set L of lead heads such that if a 2nds place method has lead heads L then its nths place version also has lead heads L.

I'm not sure whether I knew that explicitly. It's quite easy to see: for example, consider a 2nds place minor method and think about the last lead of the course, which produces 123456 as the final lead head. Ringing a 6ths place lead end instead of 2nds place would produce 142635, which generates the set of Plain Bob lead heads. So if the 6ths place version is to have the same lead heads as the 2nds place version, then that set of lead heads must be the Plain Bob lead heads.

It seems more or less equivalent to the observation that the lead heads and lead ends of Plain Bob, with the treble removed, form plain hunting.

Simon



On 8 Feb 2012, at 10:06, Robin Woolley wrote:

> I agree with Simon Gay - I use 'regular' to mean a method with plain-bob
> lead-heads.
>
> Why are non-plain-bob lead-heads irregular in my book?  For one reason
> taking Minor as an example, 2nds place and 6ths place irregular methods have
> different lead-ends sets:
>
> 2nds place: {63542, 56423, 32654, 45236}
> 6ths place: {25634, 43265, 56423, 64352}
>
> A consequence of this is that the lead-ends of plain bob are 'regular' also.
>
> 'regular' can have several meanings, of course. 'usual' is probably closest.
> (CUP on-line)
>
> Best wishes
> Robin
>
>
>
> _______________________________________________
> ringing-theory mailing list
> ringing-theory at bellringers.net
> http://bellringers.net/mailman/listinfo/ringing-theory_bellringers.net


The University of Glasgow, charity number SC004401