The Composition of Peals in Parts

Brian D Price

 

The device which enables us to compose extents with facility is subdivision into parts. This applies from the simplest examples, the plain hunt on 3 bells and Plain Bob Minimus on 4 (both palindromic 3-part extents) to tough problems like composing peals of Stedman Triples. The simplest sets of partheads are cyclic, with a number of working bells rotating among themselves, but there are many more-complex sets of partheads which may be used for composition. In general, we need a group.

Groups were formalised by mathematicians (notably by Lagrange and Cayley) in the 19th century, yet ringers were using them 200 years before that. In ringing we are concerned with groups of permutations, or 'perms', as partheads. The usual term 'rows' will be avoided in this paper, as it will be used in another context. There are in general four criteria for checking a group, but for groups of perms there is but one for which we need to test: closure.

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Contributed by: Brian D.Price, 19 Snarsgate Street, LONDON W10 6QP. Contents page for WWW by Don Morrison