2024/10/31 by Ragnar Freij-Hollanti, Freij-Hollanti, Ragnar, Patricija Šapokaitė +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #Bioinformatics and Genomic Networks #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #Data Visualization and Analytics #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2410.23932
openalex publication_date 2024/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a novel definition of hypergraphical matroids, defined for arbitrary hypergraphs, simultaneously generalizing previous definitions for regular hypergraphs (Main, 1978), and for the hypergraphs of circuits of a matroid (Freij-Hollanti, Jurrius, Kuznetsova, 2023). As a consequence, we obtain a new notion of cycles in hypergraphs, and hypertrees. We give an equivalence relation on hypergraphs, according to when their so-called matroidal closures agree. Finally, we characterize hypergraphs that are isomorphic to the circuit hypergraphs of the associated matroids.