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Distinguishing partitions of complete multipartite graphs
A \textit{distinguishing partition} of a group with automorphism group
is a partition of that is fixed by no nontrivial element of
. In the event that is a complete multipartite graph with its
automorphism group, the existence of a distinguishing partition is equivalent
to the existence of an asymmetric hypergraph with prescribed edge sizes. An
asymptotic result is proven on the existence of a distinguishing partition when
is a complete multipartite graph with parts of size and
parts of size for small , and large , . A key tool
in making the estimate is counting the number of trees of particular classes
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