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erdős #497 · Dedekind's problem

← #496 · #498 → (packet.json; erdosproblems.com)

How many antichains in $[n]$ are there? That is, how many families of subsets of $[n]$ are there such that, if $F$ is such a family and $A, B \in F$ , then $A \neq \subseteq B$ ?

Worked, still open.

combinatorics · solved · 0 attempts

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A000372 — Dedekind numbers or Dedekind's problem: number of monotone Boolean functions of n variables, number of antichains of subsets of an n-set, number of elements in a free distributive lattice on n generat2,3,6,20,168,7581,7828354,2414682040998,56130437228687557907788,286386577668298411128469151667598498812366

links

Sperner's theorem · reference

Create a formalisation here · link

status

solved

finding.noted · reviewer:will-blair · 1 day

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