Abstract
A sunflower is a collection of sets {U1,…,Un} such that the pairwise intersection Ui∩Uj is the same for all choices of distinct i and j. We study sunflowers of convex open sets in Rd, and provide a Helly-type theorem describing a certain “rigidity” that they possess. In particular we show that if {U1,…,Ud+1} is a sunflower in Rd, then any hyperplane that intersects all Ui must also intersect ⋂i=1d+1Ui. We use our results to describe a combinatorial code Cn for all n≥2 which is on the one hand minimally non-convex, and on the other hand has no local obstructions. Along the way we further develop the theory of morphisms of codes, and establish results on the covering relation in the poset PCode.
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 callDisclaimer: 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.
