Language-model proof of the Daykin–Frankl conjecture
- Mathematics
For every convex P in the Boolean lattice Q_n and all k≥0, w(P×Q_k)≥w(Q_{n+k})|P|/2^n. The k=0 case proves the Daykin–Frankl relative-width conjecture.
Daykin–Frankl conjecture on convex Boolean-lattice subsets
- Mathematics
For every convex subset P of the n-dimensional Boolean lattice, its largest antichain occupies at least the same fraction of P as the central layer occupies of the full lattice.
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Understand the problem ↓Understanding the problem
Read the background
For every convex subset P of the n-dimensional Boolean lattice, its largest antichain occupies at least the same fraction of P as the central layer occupies of the full lattice.
Why it matters
The conjecture asks whether convexity preserves a universal lower bound on the relative width of a Boolean-lattice subset.
What counts as progress
Does every convex P in Q_n satisfy w(P)/|P| ≥ binom(n, floor(n/2))/2^n?
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