[r-t] Bobs-only Stedman Triples - 66 complete B-block peals

Andrew Johnson andrew_johnson at uk.ibm.com
Sat Apr 23 11:35:08 BST 2022

66 complete B-block peals

I have found over 500 sets of round B-blocks which together with some B-blocks exactly cover the extent in an odd number [47 to 71] of round blocks where the sixes can be rearranged to give 66 complete B-blocks. Some of the sets of blocks are given below together with some peals.

47 round blocks, signature 39:2+53

https://complib.org/composition/85935 585 bobs, irregular 3-part
https://complib.org/composition/96222 594 bobs, 3-part
https://complib.org/composition/96220 591 bobs, 3-part

51 round blocks, signature 36:3+57

https://complib.org/composition/78043 606 bobs

63  round blocks, signature 32:7+51

c 5040!63 
https://complib.org/composition/88097 612 bobs
https://complib.org/composition/91434 573 bobs

The 3-part peals make a change from the one-part peals. There are several types of 3-part peals:

Exact 3-parts: all the parts are called the same.

Other 3-parts:
Blocks which divide the extent into 3 identical parts. These are then linked with Q-sets of bobs or omits. For an easier peal it is best to use only 1 Q-set (or perhaps a second at a similar point in other parts). The sixes affected by the Q-set should be as close a possible to minimise the disruption. If the 3 identical parts are divided into ABCD at the Q-set points then peals of the form
where ' is a bob or omit can sometimes be found. We should minimise the length of B and C.
So the peal links the parts like this (view in a fixed pitch font):
1234567: ABC
1357246: ..CD
1357246: AB
1526374: .BCD
1526374: A
1234567: ...D

A variation is
which might be easier to call, at the expense of a longer first part and shorter second and third parts.

It might be possible to add extra Q-sets of omits to reduce the bob count, but the peal is then less regular.

Sometime the extent can be split into round blocks using a group of order 3, but not into 3 identical parts, but in 2,3,4,5.. sets of 3 identical parts. If there are an odd number of sets then it might be possible to find some Q-sets of bobs or omits to link everything together.

Irregular 3-parts
By bobbing all available Q-sets there might be whole B-blocks revealed as some of the sets. If complementary pairs of B-blocks are then available a free choice of 1 of the 6 possible pairs can be made, and that might give more Q-sets of omits to link everything together. The result is going to be a much less regular peal though.

With all these 3-part peals then by choosing an appropriate rotation/reversal a good part-end (either 1357246 or 3456127 etc.) can often be found.

To be continued.

Andrew Johnson

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