Record compositions of alternating permutations and noncommutative symmetric functions

This repository contains artifacts generated by AxiomProver related to the paper arXiv:2607.12873.

Input files

• input/task.md: problem statement

Output files

• RecordCompositions/problem.lean: translation of the problem statement into Lean 4.31.0
• RecordCompositions/solution.lean: solution in Lean 4.31.0

One can verify that the problem.lean and solution.lean are compatible using the axle verify-proof command:

cd $DIRECTORY
axle verify-proof --environment lean-4.31.0 problem.lean solution.lean | jq ".okay"

Formalization notes

NSym and Sym are modeled directly following the paper rather than derived from Mathlib, which lacks the structures required for this work.

Lean version

The formal proofs provided in this work were developed and verified using Lean 4.31.0. Compatibility with earlier or later versions is not guaranteed due to the evolving nature of the Lean 4 compiler and its core libraries.

License

This repository uses the MIT License. See LICENSE for details.

Repository maintainers

• Evan Chen
• Kenny Lau
• Michal Mogielnicki
• Ken Ono
• Jujian Zhang