2025/12/02 by Guterman, Lazar, Nevo, Eran
#05B35 #05C65 #05E45 #13F55 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2512.03294
We characterize the shifted simple graphs and the 3-uniform shifted 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. For symmetric shifting, we prove an analogous characterization for shifted simple graphs, where the classical generic rigidity matroid is an example of a matroid arising in this way.