Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Amini, Omid, Gierczak, Lucas
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4393939963