Researchers have constructed an explicit counterexample to a conjecture made by Stanley regarding differential posets. For every r greater than or equal to 3, they developed an r-differential poset P^(r) where the cardinality of its fourth rank is less than that of Y^r, the r-fold Cartesian power of Young's lattice. Specifically, for r=3, the construction modifies rank-four lower-cover blocks of Y^3 to achieve a different initial rank sequence. AI
RANK_REASON Academic paper published on arXiv presenting a mathematical counterexample. [lever_c_demoted from research: ic=1 ai=0.1]
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