Ordered partition posets with block sizes divisible by d are Cohen-Macaulay with explicitly computed symmetric-group homology, and the modulo-1 variant has Catalan Möbius functions.
Cohen- M acaulay ordered sets
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Ordered set partition posets
Ordered partition posets with block sizes divisible by d are Cohen-Macaulay with explicitly computed symmetric-group homology, and the modulo-1 variant has Catalan Möbius functions.