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Flattened Stirling Permutations
Recall that a Stirling permutation is a permutation on the multiset
such that any numbers appearing between repeated
values of must be greater than . We call a Stirling permutation
``flattened'' if the leading terms of maximal chains of ascents (called runs)
are in weakly increasing order. Our main result establishes a bijection between
flattened Stirling permutations and type set partitions of
, which are known to be enumerated by the
Dowling numbers, and we give an independent proof of this fact. We also
determine the maximal number of runs for any flattened Stirling permutation,
and we enumerate flattened Stirling permutations with a small number of runs or
with two runs of equal length. We conclude with some conjectures and
generalizations worthy of future investigation.Comment: 15 pages, 1 figure, 2 tabl