Counting Linear Extensions Below the $2^n$ Barrier
Koivisto asked at Dagstuhl in 2013 whether the linear extensions of an arbitrary $n$-element poset can be counted exactly in time $O^*(c^n)$ for some $c < 2$. Yes: a deterministic exact algorithm runs in $O^*(1.89^n)$, breaking the $2^n$ barrier for the general problem.
Exact FrontierDelta
Scope and record
Occurred: Aug 19, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.
Canonical aliases: Counting Linear Extensions Below the $2^n$ Barrier · Linear extensions, $2^n$ barrier
Confidence: Not scored
Registry verification: unreviewed · preprint · candidate
Attribution
VibeMathed
registry · event recorded by
Keigo Oka
human · human collaborator
Claude Opus 5
model · ai model contributor · Anthropic
ChatGPT 5.6 Sol
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Keigo Oka
This event attributed to ChatGPT 5.6 Sol
This event attributed to Claude Opus 5