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.
Saturation for sums of posets and antichains.Preprint, arXiv ref:2509.10294
2 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.
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.