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.
A simple upper bound on the number of antichains in[t]n.Order, 36(3):507–510
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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.