# CombEval: A Framework for Evaluating Combinatorial Counting in Large Language Models

arXiv: https://arxiv.org/abs/2606.19788 · HTML: https://mlsanity.com/paper/2606.19788/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 22 of 22)

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- [CombiBench: Benchmarking LLM Capability for Combinatorial Mathematics](https://mlsanity.com/paper/2505.03171/) (2025)
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- [Lifted Inference with Linear Order Axiom](https://mlsanity.com/paper/2211.01164/) (2022)
- [MathGAP: Out-of-Distribution Evaluation on Problems with Arbitrarily Complex Proofs](https://mlsanity.com/paper/2410.13502/) (2024)
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## Abstract (arXiv)

We present CombEval, a dynamic benchmark for evaluating combinatorial counting in large language models. CombEval represents each problem as a typed Cofola specification over entities, combinatorial objects, object dependencies, and constraints, enabling controlled generation of natural-language counting problems with exact solver-verified answers. Unlike static collections, CombEval supports systematic variation of object type, entity scale, constraint count, and reasoning depth. We evaluate 11 LLMs under direct and code-augmented settings and find that models remain brittle on ordered objects, indistinguishable elements, relatively positional constraints, and nested object dependencies. Error analysis further identifies failures in constraint interpretation and counting principles. CombEval provides a diagnostic testbed for studying when and why LLMs fail at combinatorial reasoning. The code and generated benchmark suites are publicly available at https://github.com/YuxuZhou-CN/combination-problem-generation.