Every n-element poset embeds into a poset of size at most 2^(2n/3 + C*sqrt(n)), improving the folklore 2^n upper bound for universal posets.
The theory of partitions
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Smaller universal posets
Every n-element poset embeds into a poset of size at most 2^(2n/3 + C*sqrt(n)), improving the folklore 2^n upper bound for universal posets.