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Mathematicians Disprove Stanley's Rankwise Lower-Bound Conjecture for Differential Posets

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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]

Read on arXiv cs.AI →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Mathematicians Disprove Stanley's Rankwise Lower-Bound Conjecture for Differential Posets

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Academic paper published on arXiv presenting a mathematical counterexample. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

  1. arXiv cs.AI TIER_1 English(EN) · Xinan Dai, Yuchen Yang, Wenhao Deng, Yingdong Shi, Tailin Wu ·

    An Explicit Counterexample to Stanley's Rankwise Lower-Bound Conjecture for Differential Posets

    arXiv:2607.22988v1 Announce Type: cross Abstract: In Problem~6 of his 1988 paper on differential posets, Stanley asked for the least possible cardinality of a fixed rank of an $r$-differential poset and suggested that the minimum should be attained by $Y^r$, the $r$-fold Cartesia…

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