[r-t] Definitions so far

Dale Winter moikney at gmail.com
Sat Jan 17 13:19:21 UTC 2015

> >Method: A process for generating a sequence of Changes at a given Stage
> As I tried to explain before, I think this one is absolutely nuts.  I think a method should be defined simply as a sequence of changes, not an (ill-defined) process for generating it.

I’m not sure that the process needs to be ill defined. Certainly it seems that \alpha and \beta methods can be codified formally, no?

Let S_N denote the permutation group on N letters. Let T_N be the set of finite nonempty sequences in S_N. 

Definition: An \alpha method is a function S_N -> T_N.

(we think of the first change in S_N as the lead end and the subsequent sequence as the changes (not rows) you ring after that lead end)

Definition: An \alpha method m is also \beta if it is a constant function; m(i) = m(j) for all i, j in S_N. Equivalently a beta method is a finite sequence of changes.

So long as we start at rounds \alpha method is a stupid notion, agreed. If you splice in at some other row it seems to me that these concepts are different and each potentially interesting?


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