[r-t] Notating jump changes (was Blue line (/grid) generators / Jump Changes)
Alexander Holroyd
holroyd at math.ubc.ca
Tue May 19 07:53:08 UTC 2015
On Sun, 17 May 2015, Don Morrison wrote:
> On Mon, Mar 23, 2015 at 6:46 AM, Alexander Holroyd <holroyd at math.ubc.ca> wrote:
>> On notation, since jump methods tend to have relatively few and small jumps,
>> I like using (xy) for a jump from place x to place y (where |x-y|>=2), and
>> as usual z for zths place made, so e.g.
>>
>> (13)4 denotes
>> 23146587
>>
>> (13)(31)8 or (13)(31) denotes
>> 32154768
>>
>> (13)(42) denotes
>> 24136587
>>
>> I think it's true (but perhaps not completely obvious) that there is always
>> at most one way to fill in the remainder of such a change with non-jumping
>> bells.
>
> Yes and no.
>
> Consider your (13)(31) example. But expand it to (15)(51). Is that now
> 52431768 or 53241768? If we say "oh, you only have to specify the
> stuff in between if it's not uniquely determined" that not only gets a
> little fuzzy, it is, I think, contrary to usual practice with normal
> place notation where I don't think most folks would ever write 35
> instead 345 or 3458.
>
> Or should (13)(31) instead be (13)2(31)?
>
> And is (13)2(31) really any clearer than 32154768? It's no shorter for
> major, a little longer for doubles, and significantly shorter for
> sixteen. I guess it does have one big benefit, though, in that it
> applies without change to all stages minimus and above.
>
Good point. I guess the "2" is needed. Personally I like (13)2(31)
much better than 32154768, for reasons along the lines you mention.
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