[r-t] Mega-tittums (again)

[Alexander Holroyd]

On Fri, 16 Jan 2015, Philip Earis wrote:

> As the overall aim here is to get all 480 run rows, I’m tempted to 
> generalise and rephrase accordingly...what’s the shortest length 
> 8-part anyone can produce which contains all 480 runs? Elegance and 
> maximal symmetry are desirable.
>
If that's really what you want, then the minimum length is something like 
784 (e.g. see below), but I don't think you would want to ring it, and the 
"desiderata" are likely impossible to achieve.  It wouldn't be too hard to 
pad it to 2-3 times the length and somewhat more sensible, although I 
don't think it would become a classic.  For that one needs to makes some 
decisions about what structure to impose.

TRUE.
Comes round after
784 rows.

24 *5678.
24 *8765.
24 5678*.
24 8765*.

                : 12345678            *5678 *8765 5678* 8765*
part[A[345678  : 21345678 1          1     .     .     .
        145678  : 23145678 2          1     .     .     .
        345678  : 32145678 3          1     .     .     .
        145678  : 31245678 4          1     .     .     .
        345678  : 13245678 5          1     .     .     .
        5678    : 31425678 6          1     .     .     .
        345678  : 13425678 7          1     .     .     .
        145678  : 14325678 8          1     .     .     .
        345678  : 41325678 9          1     .     .     .
        145678  : 43125678 10         1     .     .     .
        345678] : 34125678 11         1     .     .     .
      -         : 43216587 12         .     .     .     .
      B[123456  : 43216578 13         .     .     .     .
        123458  : 43216758 14         .     .     .     .
        123456  : 43216785 15         .     .     .     .
        123458  : 43216875 16         .     .     .     .
        123456  : 43216857 17         .     .     .     .
        1234    : 43218675 18         .     .     .     .
        123456  : 43218657 19         .     .     .     .
        123458  : 43218567 20         .     .     .     .
        123456  : 43218576 21         .     .     .     .
        123458] : 43218756 22         .     .     .     .
      123456    : 43218765 23         .     1     .     .
      A         : 21438765 34         .     11    .     .
      -         : 12347856 35         .     .     .     .
      B         : 12345687 45         .     .     .     .
      123478    : 12346587 46         .     .     .     .
      B         : 12348756 56         .     .     .     .
      123456    : 12348765 57         .     1     .     .
      A         : 34128765 68         .     11    .     .
      -         : 43217856 69         .     .     .     .
      B         : 43215687 79         .     .     .     .
      123456    : 43215678 80         1     .     .     .
      A         : 21435678 91         11    .     .     .
      link[167  : 24153678 92         .     .     .     .
           -    : 42516387 93         .     .     .     .
           1    : 45261837 94         .     .     .     .
           -    : 54628173 95         .     .     .     .
           3    : 45682713 96         .     .     .     .
           1478 : 46587213 97         .     .     .     .
           1]]  : 45678123 98         .     .     .     .
part           : 78123456 196        .     .     .     .
part           : 23456781 294        .     .     .     .
part           : 56781234 392        .     .     1     .
part           : 81234567 490        .     .     23    24
part           : 34567812 588        .     .     .     .
part           : 67812345 686        .     .     .     .
part           : 12345678 784 Rounds 1     .     .     .