# Mapping Uncharted Symmetries: Machine Discovery in Combinatorics

arXiv: https://arxiv.org/abs/2605.19063 · HTML: https://mlsanity.com/paper/2605.19063/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 12 of 12)

- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [The Lean mathematical library](https://mlsanity.com/paper/1910.09336/) (2019)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [Aristotle: IMO-level Automated Theorem Proving](https://mlsanity.com/paper/2510.01346/) (2025)
- [Constructions in combinatorics via neural networks](https://mlsanity.com/paper/2104.14516/) (2021)
- [Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers](https://mlsanity.com/paper/2410.08304/) (2024)
- [Easy Learning from Label Proportions](https://mlsanity.com/paper/2302.03115/) (2023)
- [Is deep learning a useful tool for the pure mathematician?](https://mlsanity.com/paper/2304.12602/) (2023)
- [Neurosymbolic Programming for Science](https://mlsanity.com/paper/2210.05050/) (2022)
- [Learning from Label Proportions: Bootstrapping Supervised Learners via Belief Propagation](https://mlsanity.com/paper/2310.08056/) (2023)
- [Even with AI, Bijection Discovery is Still Hard: The Opportunities and Challenges of OpenEvolve for Novel Bijection Construction](https://mlsanity.com/paper/2511.20987/) (2025)
- [From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithm](https://mlsanity.com/paper/2511.12421/) (2025)

## Built on by (most cited first, 1 of 1)

- [AI Discovery in Combinatorics: From Problems to Solutions and Back to Bigger Problems](https://mlsanity.com/paper/2610.16555/) (2026)

## Abstract (arXiv)

Inspired by long-standing open problems in algebraic combinatorics, we show that modern machine learning can meaningfully contribute to verifiable mathematical discoveries. In particular, we focus on the construction of simple mathematical functions under exact distributional constraints, a setting we formalize as Simple Learning Under Rigid Proportions (SLURP). We tackle this problem by introducing two methods: MapSeek-Functional, which models the desired function alternating pseudo-labeling and supervised training steps; and MapSeek-Symbolic, designed to directly produce symbolic formulas. We successfully apply both methods to a research problem in algebraic combinatorics, discovering a new combinatorial interpretation of the q,t-Narayana polynomials arising from representation theory. To our knowledge, this is the first such interpretation based on noncrossing partitions. Using one discovered statistic, we find a combinatorial proof of the symmetry of these polynomials in a previously unsolved case. To streamline verification and reproducibility, we release all code, including a formalization of all the mathematical discoveries of this paper in Lean 4.