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Recent related table search methods leverage tabular representation learning and language models to encode tables into vector representations for efficient semantic search. The main challenge of these models is to retain essential structural properties of tabular data. Graph-neural networks have shown to be efficient in solving certain challenges like row/column permutation sensitivity and multi-table representation. In this context, we present HEARTS, a related-table search system powered by HyTrel, a hypergraph-enhanced Tabular Language Model (TaLM). By representing tables as hypergraphs with cells as nodes and rows, columns, and tables as hyperedges, HyTrel preserves relational properties such as row and column order invariance, making it a robust solution for related table search tasks.