A new necessary condition is established that Y must be partition-transitive w.r.t. certain partitions of n for (T_n, Y) to tile S_n, generalizing Rothaus-Thompson and Nomura, with a conjecture that neither T_n nor T_n* tiles S_n for n >= 4.
Zieschang, Cayley graphs of finite groups, J
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Tiling the symmetric group by transpositions
A new necessary condition is established that Y must be partition-transitive w.r.t. certain partitions of n for (T_n, Y) to tile S_n, generalizing Rothaus-Thompson and Nomura, with a conjecture that neither T_n nor T_n* tiles S_n for n >= 4.