Séminaire Lotharingien de Combinatoire, 95B.10 (2026), 12 pp.
Lazar Guterman and Eran Nevo
Matroids Arising from Algebraic Shifting
Abstract.
We characterize the shifted simple graphs and the shifted 3-uniform hypergraphs whose inverse image under exterior shifting is the set of bases of a matroid:
those are exactly the
hypergraphs whose hyperedges form an initial lex-segment. There are
several examples of known matroids arising in this way: the simplicial
matroid, the hyperconnectivity matroid and the area-rigidity
matroid. For k≥4, we provide a similar characterization for
shifted k-uniform hypergraphs satisfying an additional
combinatorial condition.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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