*(Mathematics of Campanology)*

Brian D. Price.

January 2006

Three versions of the paper are available:

- Scan of the original paper printed by Brian Price (10MB pdf)
- HTML version of the paper (best for viewing on-line)
- New pdf version (1.7MB) produced from the HTML version (best for printing out)

The scan of Brian Price’s original paper (10MB pdf) was provided by Andrew Johnson in April 2017, together with the following commentary:

“At the time (31 January 2006) Brian replied to my comments on the paper saying:

Dear Andrew - Thanks for your E-mail.
Yes, a major error in stating “original triples” instead of “original minor”! Philip Saddleton has pointed that out, too. He also told me about an article in American Mathematical Monthly of February 1999, of another proof of Rankin's theorem. I obtained a photocopy of it, but I can't understand the terminology - up to date Group theory - it seems to delegate the proof to a textbook theorem. I’m all for simple stuff! I think I’ll have to re-issue the paper, with OT corrected and mention of the 1999 article. Also, I wasn’t satisfied with the printing of my ink-jet printer. Someone sometime should re-vamp my list of permutation groups, as several omissions of sub-groups and the like have turned up. Why not you? I don’t claim any particular originality over what I did! Regards, B.D.P. |

but I don't think he published an update with a correction to ‘original triples’ on page 9 or a mention of:

Swan, Richard G.
**A Simple Proof of Rankin's Campanological Theorem.** The American Mathematical Monthly, vol. 106, no. 2, (Feb., 1999), pp. 159–161. (JSTOR)”

The HTML version was produced by Andrew Johnson in October 2017 from the original paper copy he held, specifically to make it more accessible and easier to read. As part of this exercise, Andrew corrected the original triples/minor

error and added many links for the cross references in the text and the listed References at the end. During proof reading, it was also noted that there was a slight difference between the text of a
1949 letter written by Brian Price to *The Ringing World* and his quotation of the same letter in this 2006 paper. The 1949 text seems a little clearer, and it is that that has been used in the HTML version.

The new pdf version was produced from the HTML version as an equivalent to the original paper with the page number cross-references updated.

Peter Blight
*last updated 14 December 2017*