2024/04/02 by Omid Amini, Amini, Omid, Lucas Gierczak +1 · 1 citation
Engineering · Biochemistry, Genetics and Molecular Biology · Mathematics · #graph theory and CDMA systems #Genome Rearrangement Algorithms #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2404.01971
We introduce combinatorial objects named matricubes that provide a generalization of the theory of matroids. As matroids provide a combinatorial axiomatization of hyperplane arrangements, matricubes provide a combinatorial axiomatization of arrangements of initial flags in a vector space. We give cryptomorphic axiomatic systems in terms of rank function, flats, circuits, and independent sets, and formulate a duality concept. We also provide precise links between matricubes, permutation arrays and matroids, and raise several open questions.