Problem dossier · Combinatorics
Dedekind numbers
D(n) counts the antichains of subsets of an n-element set — equivalently, monotone Boolean functions on n variables. Compute the next value.
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Status
D(9) was computed in 2023 (two independent teams, 42 digits). D(10) is unknown.
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The Angle of Attack
Study symmetry-reduction and interval-counting techniques that cracked D(9); estimate D(10) via sampling and asymptotic (Korshunov) formulas; hunt structure in the growth sequence.
Tags: boolean functions · antichains · enumeration · lattice
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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