Threshold functions for incidence properties in finite vector spaces |
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| Affiliation: | 1. Korea Institute for Advanced Study (KIAS), Republic of Korea;2. Discrete Mathematics Group, Institute for Basic Science (IBS), Republic of Korea;3. University of Science, Vietnam National University, Hanoi, Viet Nam;1. Department of Mathematics and Computer Science, Santa Clara University, 500 El Camino Real, 95053, USA;2. Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada;1. Department of Mathematics, Chungbuk National University, Republic of Korea;2. University of Science, Vietnam National University, Hanoi, Viet Nam;3. Department of Mathematics, National Taiwan University, Taiwan;1. School of Mathematical Sciences, Hebei Workstation for Foreign Academicians, Hebei Normal University, Shijiazhuang 050024, PR China;2. Chelyabinsk State University, 129 Bratiev Kashirinykh st., Chelyabinsk 454021, Russia;3. Department of Mathematics, University of British Columbia, Vancouver V6T 1Z2, Canada |
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| Abstract: | The main purpose of this paper is to provide threshold functions for the events that a random subset of the points of a finite vector space has certain properties related to point-flat incidences. Specifically, we consider the events that there is an ℓ-rich m-flat with regard to a random set of points in , the event that a random set of points is an m-blocking set, and the event that there is an incidence between a random set of points and a random set of m-flats. One of our key ingredients is a stronger version of a recent result obtained by Chen and Greenhill (2021). |
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| Keywords: | Incidences Rich-flats Blocking sets Collinear triples |
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