The Q-set Parity Law

A Review of its Proofs from Thompson's of 1886

(Mathematics of Campanology)

Brian D. Price.
January 2006

This scan of Brian Price’s 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!


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

R. G. Swan. A simple proof of Rankin's campanological theorem. The American Mathematical Monthly, 106(2):159-161, February 1999.”

Clearly, Brian Price was keen for his papers to be accessible to anyone who might be interested, and it would be very good to have an html version and a clean text version that could be downloaded as a pdf, but it seems unlikely that Brian’s original soft copy survives. If, however, anyone could provide a soft copy please and I will make it available here.

Peter Blight, May 2017