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The Count Broke the Two-to-the-N Barrier
A deterministic algorithm counted linear extensions of arbitrary partial orders in O*(1.89^n) time.
Summary
A deterministic algorithm counted linear extensions of arbitrary partial orders in O*(1.89^n) time.
A linear extension orders every element of a partial order without violating its constraints. The new algorithm splits the problem by chain structure and, near an antichain, records only the first comparable element above each selected element before using a compressed dynamic program. Its O*(1.89^n) bound beats the long-standing 2^n general barrier and addresses a question posed in 2013. The result is theoretical, with a verification script supplied as an ancillary artifact.
Why it matters
A deterministic algorithm counted linear extensions of arbitrary partial orders in O*(1.89^n) time.
Limits and context
- The new algorithm splits the problem by chain structure and, near an antichain, records only the first comparable element above each selected element before using a compressed dynamic program.
Key claims
A deterministic algorithm counted linear extensions of arbitrary partial orders in O*(1.89^n) time.
Qualification: The new algorithm splits the problem by chain structure and, near an antichain, records only the first comparable element above each selected element before using a compressed dynamic program.
Evidence: source-2026-08-21-016
Sources
- arXiv preprint 2608.19505arXiv · primary research
Corrections
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