Autoformalization aims to bridge the gap between human mathematical intuition and formal proof by automating the translation of informal reasoning into machine-verifiable languages.Despite significant breakthroughs catalyzed by Large Language Models (LLMs), autoformalizing Combinatorics remains a formidable challenge due to its intricate structural dependencies and the severe scarcity of high-quality formal datasets.To address these challenges, we propose SAIR-Comb, a Structure-Aware Iterative Refinement framework for Combinatorics powered by Lean 4 and LLMs.SAIR-Comb employs a multi-stage pipeline: first, it performs data augmentation and refinement by rectifying syntactic, semantic, and structural errors, guided by a curated manual combinatorics dataset.The model then undergoes a two-stage training regime: expert iteration with syntactic grounding, followed by reinforcement learning (RL) to align formal reasoning trajectories.Furthermore, we introduce Structural Consistency-a rigorous new metric designed to expose formalizing failures that elude traditional semantic-only evaluations.Experiments demonstrate that SAIR-Comb achieves strong performance on the specialized CombiBench while remaining highly competitive on general-domain benchmarks, including PutnamBench and ProverBench.