Elizalde-Luo Pattern-Avoidance Conjecture

Is the number of nonnesting permutations of $\{1,1,\dots,n,n\}$ avoiding both $1132$ and $3312$ equal to $3^n - 3 \cdot 2^{n-1} + 1$ for every $n \ge 1$ ?

Result: Proved
Status: Resolved
AI contribution: AI-discovered
Method: Argument
Field: Enumerative combinatorics
Posed by: Sergi Elizalde & Luo
Year posed: 2025
Years open: 1y
Solved: 2026-07-12
Model: Demonstrandum multi-agent pipeline
Vendor: —
Collaborators: —
Verification: Lean-verified
Publication: Announced
Significance: 5 / 100
Disclosed cost: —
Wikipedia: No dedicated article

What the AI did

Found by the Demonstrandum multi-agent pipeline; every refutation ships a finite certificate, a mutation-tested checker, and an independent clean-room recomputation.

Verification

Proved and Lean-checked end to end; not externally refereed.

Source

Demonstrandum artifacts repository (RESULTS.md)

Elizalde-Luo Pattern-Avoidance Conjecture

What the AI did

Verification

Source

Discussion