For every poset P, the induced saturation function sat*([t]^n, P) is either eventually constant or Omega(sqrt(n)) as n grows, with chains constant and unique-twin-cover posets growing.
Gluing posets and the dichotomy of poset saturation numbers.Preprint, arXiv ref:2503.12223
3 Pith papers cite this work. Polarity classification is still indexing.
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The saturation number for the diamond poset is exactly n+1.
The induced saturation number sat*(n, N) is at least (n+6)/4.
citing papers explorer
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Induced poset saturation in the hypergrid
For every poset P, the induced saturation function sat*([t]^n, P) is either eventually constant or Omega(sqrt(n)) as n grows, with chains constant and unique-twin-cover posets growing.
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The Exact Saturation Number for the Diamond
The saturation number for the diamond poset is exactly n+1.
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Linear Saturation for $\mathcal N$ via Butterflies
The induced saturation number sat*(n, N) is at least (n+6)/4.