Abstract

Let H → G be a strong map between two combinatorial geometries on the same set X . The rank function, flats, and independent sets of G are characterized in terms of a factorization of E → G into elementary strong maps. When H is the free geometry on X , these results lead to a representation of G as the “basis intersection” of a family of transversal geometries (in the sense that B is a basis for G if and only if B is a basis for each of the transversal geometries in the family), and dually, as the basis intersection of a family of principal geometries.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.