For every n >= k >= 2, the matching polynomial of an n-vertex k-uniform hypergraph is uniquely determined by the multiset of induced subgraphs on floor((k-1)/k n)+1 vertices.
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Reconstructing hypergraph matching polynomials
For every n >= k >= 2, the matching polynomial of an n-vertex k-uniform hypergraph is uniquely determined by the multiset of induced subgraphs on floor((k-1)/k n)+1 vertices.