Bell-ringing sequences

N. J. A. Sloane njas at research.att.com
Sun Jan 25 04:49:17 CET 2004


Dear Seqfans,
I added 8 sequences from "Plain Bob Minimus" in bell-ringing, see below.
This is a change-ringing method for 4 bells.

I would like to get further sequences of this type,
if someone would be willing to work them out.
There are many possibilities: Treble Bob, Stedman Triples, ...

The links below give further information.

With n bells, the sequences have period n!, so 5-bell sequences would just fit; 
for 6 or more bells it will only be possible to give the beginning of the sequences.

It would be nice if some seq-fan would pick up the bell here
and run with it.

NJAS

%I A090277
%S A090277 1,2,2,4,4,3,3,1,1,3,3,2,2,4,4,1,1,4,4,3,3,2,2,1,1,2,2,4,4,3,3,1,1,
%T A090277 3,3,2,2,4,4,1,1,4,4,3,3,2,2,1,1,2,2,4,4,3,3,1,1,3,3,2,2,4,4,1,1,4,
%U A090277 4,3,3,2,2,1,1,2,2,4,4,3,3,1,1,3,3,2,2,4,4,1,1,4,4,3,3,2,2,1,1,2,2
%N A090277 "Plain Bob Minimus" in bell-ringing is the sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives number in position 1 of n-th permutation.
%H A090277 Rober Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a>
%H A090277 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html">Application: Bell Ringing</a>
%H A090277 M.I.T. Bell-Ringers, <a href="http://web.mit.edu/bellringers/www/html/change_instruction.html">General Information On Change Ringing</a>
%F A090277 Period 24.
%e A090277 The full list of the 24 permutations is as follows (the present sequence gives the first column):
%e A090277 1 2 3 4
%e A090277 2 1 4 3
%e A090277 2 4 1 3
%e A090277 4 2 3 1
%e A090277 4 3 2 1
%e A090277 3 4 1 2
%e A090277 3 1 4 2
%e A090277 1 3 2 4
%e A090277 1 3 4 2
%e A090277 3 1 2 4
%e A090277 3 2 1 4
%e A090277 2 3 4 1
%e A090277 2 4 3 1
%e A090277 4 2 1 3
%e A090277 4 1 2 3
%e A090277 1 4 3 2
%e A090277 1 4 2 3
%e A090277 4 1 3 2
%e A090277 4 3 1 2
%e A090277 3 4 2 1
%e A090277 3 2 4 1
%e A090277 2 3 1 4
%e A090277 2 1 3 4
%e A090277 1 2 4 3
%Y A090277 Cf. A090278-A090284.
%K A090277 nonn,new
%O A090277 1,2
%A A090277 njas, Jan 24 2004

%I A090278
%S A090278 2,1,4,2,3,4,1,3,3,1,2,3,4,2,1,4,4,1,3,4,2,3,1,2,2,1,4,2,3,4,1,3,3,
%T A090278 1,2,3,4,2,1,4,4,1,3,4,2,3,1,2,2,1,4,2,3,4,1,3,3,1,2,3,4,2,1,4,4,1,
%U A090278 3,4,2,3,1,2,2,1,4,2,3,4,1,3,3,1,2,3,4,2,1,4,4,1,3,4,2,3,1,2,2,1,4
%N A090278 "Plain Bob Minimus" in bell-ringing is the sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives number in position 2 of n-th permutation.
%H A090278 Rober Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a>
%H A090278 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html">Application: Bell Ringing</a>
%F A090278 Period 24.
%Y A090278 Cf. A090277-A090284.
%K A090278 nonn,new
%O A090278 1,1
%A A090278 njas, Jan 24 2004

%I A090279
%S A090279 3,4,1,3,2,1,4,2,4,2,1,4,3,1,2,3,2,3,1,2,4,1,3,4,3,4,1,3,2,1,4,2,4,
%T A090279 2,1,4,3,1,2,3,2,3,1,2,4,1,3,4,3,4,1,3,2,1,4,2,4,2,1,4,3,1,2,3,2,3,
%U A090279 1,2,4,1,3,4,3,4,1,3,2,1,4,2,4,2,1,4,3,1,2,3,2,3,1,2,4,1,3,4,3,4,1
%N A090279 "Plain Bob Minimus" in bell-ringing is the sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives number in position 3 of n-th permutation.
%H A090279 Rober Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a>
%H A090279 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html">Application: Bell Ringing</a>
%F A090279 Period 24.
%Y A090279 Cf. A090277-A090284.
%K A090279 nonn,new
%O A090279 1,1
%A A090279 njas, Jan 24 2004

%I A090280
%S A090280 4,3,3,1,1,2,2,4,2,4,4,1,1,3,3,2,3,2,2,1,1,4,4,3,4,3,3,1,1,2,2,4,2,
%T A090280 4,4,1,1,3,3,2,3,2,2,1,1,4,4,3,4,3,3,1,1,2,2,4,2,4,4,1,1,3,3,2,3,2,
%U A090280 2,1,1,4,4,3,4,3,3,1,1,2,2,4,2,4,4,1,1,3,3,2,3,2,2,1,1,4,4,3,4,3,3
%N A090280 "Plain Bob Minimus" in bell-ringing is the sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives number in position 4 of n-th permutation.
%H A090280 Rober Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a>
%H A090280 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html">Application: Bell Ringing</a>
%F A090280 Period 24.
%Y A090280 Cf. A090277-A090284.
%K A090280 nonn,new
%O A090280 1,1
%A A090280 njas, Jan 24 2004

%I A090281
%S A090281 1,2,3,4,4,3,2,1,1,2,3,4,4,3,2,1,1,2,3,4,4,3,2,1,1,2,3,4,4,3,2,1,1,
%T A090281 2,3,4,4,3,2,1,1,2,3,4,4,3,2,1,1,2,3,4,4,3,2,1,1,2,3,4,4,3,2,1,1,2,
%U A090281 3,4,4,3,2,1,1,2,3,4,4,3,2,1,1,2,3,4,4,3,2,1,1,2,3,4,4,3,2,1,1,2,3
%N A090281 "Plain Bob Minimus" in bell-ringing is the sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives position of bell 1 (the treble bell) in n-th permutation.
%C A090281 This is the "plain hunting" sequence with 4 bells.
%H A090281 Rober Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a>
%H A090281 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html"> Application: Bell Ringing</a>
%H A090281 M.I.T. Bell-Ringers, <a href="http://web.mit.edu/bellringers/www/html/change_instruction.html">General Information On Change Ringing</a>
%F A090281 Period 24.
%e A090281 The full list of the 24 permutations is as follows (the present sequence tells where the 1's are):
%e A090281 1 2 3 4
%e A090281 2 1 4 3
%e A090281 2 4 1 3
%e A090281 4 2 3 1
%e A090281 4 3 2 1
%e A090281 3 4 1 2
%e A090281 3 1 4 2
%e A090281 1 3 2 4
%e A090281 1 3 4 2
%e A090281 3 1 2 4
%e A090281 3 2 1 4
%e A090281 2 3 4 1
%e A090281 2 4 3 1
%e A090281 4 2 1 3
%e A090281 4 1 2 3
%e A090281 1 4 3 2
%e A090281 1 4 2 3
%e A090281 4 1 3 2
%e A090281 4 3 1 2
%e A090281 3 4 2 1
%e A090281 3 2 4 1
%e A090281 2 3 1 4
%e A090281 2 1 3 4
%e A090281 1 2 4 3
%Y A090281 Cf. A090277-A090284.
%K A090281 nonn,new
%O A090281 1,2
%A A090281 njas, Jan 24 2004

%I A090282
%S A090282 2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,
%T A090282 3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,
%U A090282 4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1
%N A090282 "Plain Bob Minimus" in bell-ringing is the sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives position of bell 2 in n-th permutation.
%H A090282 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html"> Application: Bell Ringing</a>
%F A090282 Period 24.
%Y A090282 Cf. A090277-A090284.
%K A090282 nonn,new
%O A090282 1,1
%A A090282 njas, Jan 24 2004

%I A090283
%S A090283 3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,
%T A090283 1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,
%U A090283 2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4
%N A090283 "Plain Bob Minimus" in bell-ringing is the sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives position of bell 3 in n-th permutation.
%H A090283 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html"> Application: Bell Ringing</a>
%F A090283 Period 24.
%Y A090283 Cf. A090277-A090284.
%K A090283 nonn,new
%O A090283 1,1
%A A090283 njas, Jan 24 2004

%I A090284
%S A090284 4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,
%T A090284 4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,
%U A090284 1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2
%N A090284 "Plain Bob Minimus" in bell-ringing is the sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives position of bell 4 (the tenor bell) in n-th permutation.
%H A090284 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html"> Application: Bell Ringing</a>
%F A090284 Period 24.
%Y A090284 Cf. A090277-A090283.
%K A090284 nonn,new
%O A090284 1,1
%A A090284 njas, Jan 24 2004






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