Abstract
A pair of partitions π 1, π 2 of a finite set S into disjoint non-empty subsets will be called conjugate if for each s∈ S, the ordered pair ( ν 1 ( s), ν 2 ( s)) determines s, where ν i ( s) denotes the cardinality of the subset of π i to which s belongs. In this note we show that S has a pair of conjugate partitions if and only if the cardinality of S is not equal to 2, 5, or 9. Partitions of this type provide a short solution to a problem arising in circuit theory.
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