Sectionable terraces and the (generalised) Oberwolfach problem

The generalised Oberwolfach problem requires v people to sit at s round tables of sizes l"1,l"2,...,l"s (where l"1+l"2+...+l"s=v) for successive meals in such a way that each pair of people are neighbours exactly @l times. The problem is denoted OP(@l;l"1,l"2,...,l"s) and if @l=1, which is the original problem, this is abbreviated to OP(l"1,l"2,...,l"s). It was known in 1892, though different terminology was then used, that a directed terrace with a symmetric sequencing for the cyclic group of order 2n can be used to solve OP(2n+1). We show how terraces with special properties can be used to solve OP(2;l"1,l"2) and OP(l"1,l"1,l"2) for a wide selection of values of l"1, l"2 and v. We also give a new solution to OP(2;l,l) that is based on Z"2"l"-"1. Solutions to the problem are also of use in the design of experiments, where solutions for tables of equal size are called resolvable balanced circuit Rees neighbour designs.

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