OEIS A000112: Unlabeled Posets and Their Surprising Connections

A deep dive into A000112, the sequence counting unlabeled partially ordered sets (posets) with n elements. We explore why the count grows so quickly, how poset structures encode nesting and crossing of factors in fixed-effects ANOVA models, and how each poset can induce a distinct T-topology via downward-closed sets. We'll visualize the 16 unlabeled posets on four elements and highlight the surprising links between order theory, statistics, and topology.

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