Abstract
Bounds are derived on the extent to which the parameter μ ( P , ∏ ) \mu (P,\,\prod ) can fail to be additive over disjoint permutations. This is done by associating an Eulerian digraph to each such pair and relating the maximum orbiticity μ ( P , ∏ ) \mu (P,\,\prod ) to the decompositions of this digraph’s arc set into arc disjoint cycles. These bounds are then applied to obtain information about the genus of the amalgamation of graphs.
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