FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3012270600> ?p ?o ?g. }

• W3012270600 abstract "We establish the following two main results on order types of points in general position in the plane (realizable simple planar order types, realizable uniform acyclic oriented matroids of rank $3$): (a) The number of extreme points in an $n$-point order type, chosen uniformly at random from all such order types, is on average $4+o(1)$. For labeled order types, this number has average $4- frac{8}{n^2 - n +2}$ and variance at most $3$. (b) The (labeled) order types read off a set of $n$ points sampled independently from the uniform measure on a convex planar domain, smooth or polygonal, or from a Gaussian distribution are concentrated, i.e. such sampling typically encounters only a vanishingly small fraction of all order types of the given size. Result (a) generalizes to arbitrary dimension $d$ for labeled order types with the average number of extreme points $2d+o(1)$ and constant variance. We also discuss to what extent our methods generalize to the abstract setting of uniform acyclic oriented matroids. Moreover, our methods allow to show the following relative of the Erdős-Szekeres theorem: for any fixed $k$, as $n to infty$, a proportion $1 - O(1/n)$ of the $n$-point simple order types contain a triangle enclosing a convex $k$-chain over an edge. For the unlabeled case in (a), we prove that for any antipodal, finite subset of the $2$-dimensional sphere, the group of orientation preserving bijections is cyclic, dihedral or one of $A_4$, $S_4$ or $A_5$ (and each case is possible). These are the finite subgroups of $SO(3)$ and our proof follows the lines of their characterization by Felix Klein." @default.
• W3012270600 created "2020-03-23" @default.
• W3012270600 creator A5021289985 @default.
• W3012270600 creator A5089352514 @default.
• W3012270600 date "2020-06-23" @default.
• W3012270600 modified "2023-09-26" @default.
• W3012270600 title "Convex Hulls of Random Order Types" @default.
• W3012270600 cites W1487872891 @default.
• W3012270600 cites W1496278954 @default.
• W3012270600 cites W1607203414 @default.
• W3012270600 cites W1620957914 @default.
• W3012270600 cites W16939786 @default.
• W3012270600 cites W176071698 @default.
• W3012270600 cites W1970823736 @default.
• W3012270600 cites W1984529618 @default.
• W3012270600 cites W2012978323 @default.
• W3012270600 cites W2022266599 @default.
• W3012270600 cites W2030260203 @default.
• W3012270600 cites W2032028171 @default.
• W3012270600 cites W2046116152 @default.
• W3012270600 cites W2050753006 @default.
• W3012270600 cites W2062072845 @default.
• W3012270600 cites W2064580310 @default.
• W3012270600 cites W2068227483 @default.
• W3012270600 cites W2072795940 @default.
• W3012270600 cites W2081680874 @default.
• W3012270600 cites W2084911775 @default.
• W3012270600 cites W2091015960 @default.
• W3012270600 cites W2117446874 @default.
• W3012270600 cites W2123689469 @default.
• W3012270600 cites W2129175815 @default.
• W3012270600 cites W2131662609 @default.
• W3012270600 cites W2134189835 @default.
• W3012270600 cites W2148713284 @default.
• W3012270600 cites W2158662841 @default.
• W3012270600 cites W2163448076 @default.
• W3012270600 cites W2205343714 @default.
• W3012270600 cites W2328860740 @default.
• W3012270600 cites W2396544646 @default.
• W3012270600 cites W2404213258 @default.
• W3012270600 cites W2606738087 @default.
• W3012270600 cites W2786519157 @default.
• W3012270600 cites W2900326533 @default.
• W3012270600 cites W2902613999 @default.
• W3012270600 cites W2905417051 @default.
• W3012270600 cites W2911399207 @default.
• W3012270600 cites W2912659905 @default.
• W3012270600 cites W2962411820 @default.
• W3012270600 cites W2962735190 @default.
• W3012270600 cites W2964204159 @default.
• W3012270600 cites W2971330320 @default.
• W3012270600 cites W2985417056 @default.
• W3012270600 cites W2987046074 @default.
• W3012270600 cites W3001411397 @default.
• W3012270600 cites W40864523 @default.
• W3012270600 cites W47661094 @default.
• W3012270600 doi "https://doi.org/10.4230/lipics.socg.2020.49" @default.
• W3012270600 hasPublicationYear "2020" @default.
• W3012270600 type Work @default.
• W3012270600 sameAs 3012270600 @default.
• W3012270600 citedByCount "1" @default.
• W3012270600 countsByYear W30122706002022 @default.
• W3012270600 crossrefType "proceedings-article" @default.
• W3012270600 hasAuthorship W3012270600A5021289985 @default.
• W3012270600 hasAuthorship W3012270600A5089352514 @default.
• W3012270600 hasConcept C10138342 @default.
• W3012270600 hasConcept C112680207 @default.
• W3012270600 hasConcept C127413603 @default.
• W3012270600 hasConcept C144133560 @default.
• W3012270600 hasConcept C182306322 @default.
• W3012270600 hasConcept C199104240 @default.
• W3012270600 hasConcept C206194317 @default.
• W3012270600 hasConcept C2524010 @default.
• W3012270600 hasConcept C33923547 @default.
• W3012270600 hasConcept C37423430 @default.
• W3012270600 hasConcept C41008148 @default.
• W3012270600 hasConceptScore W3012270600C10138342 @default.
• W3012270600 hasConceptScore W3012270600C112680207 @default.
• W3012270600 hasConceptScore W3012270600C127413603 @default.
• W3012270600 hasConceptScore W3012270600C144133560 @default.
• W3012270600 hasConceptScore W3012270600C182306322 @default.
• W3012270600 hasConceptScore W3012270600C199104240 @default.
• W3012270600 hasConceptScore W3012270600C206194317 @default.
• W3012270600 hasConceptScore W3012270600C2524010 @default.
• W3012270600 hasConceptScore W3012270600C33923547 @default.
• W3012270600 hasConceptScore W3012270600C37423430 @default.
• W3012270600 hasConceptScore W3012270600C41008148 @default.
• W3012270600 hasLocation W30122706001 @default.
• W3012270600 hasLocation W30122706002 @default.
• W3012270600 hasOpenAccess W3012270600 @default.
• W3012270600 hasPrimaryLocation W30122706001 @default.
• W3012270600 hasRelatedWork W1723055616 @default.
• W3012270600 hasRelatedWork W1823264389 @default.
• W3012270600 hasRelatedWork W2127184416 @default.
• W3012270600 hasRelatedWork W2187163417 @default.
• W3012270600 hasRelatedWork W2197902949 @default.
• W3012270600 hasRelatedWork W2950155535 @default.
• W3012270600 hasRelatedWork W2963537468 @default.
• W3012270600 hasRelatedWork W4293567948 @default.
• W3012270600 hasRelatedWork W4297913565 @default.

• next