Matches in SemOpenAlex for { <https://semopenalex.org/work/W3106683722> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W3106683722 endingPage "506" @default.
- W3106683722 startingPage "493" @default.
- W3106683722 abstract "$newcommand{LL}{mathcal{L}}newcommand{SS}{mathcal{S}}$Let (LL) be an arrangement of (n) lines in the Euclidean plane. The (k)-level of (LL) consists of all vertices (v) of the arrangement which have exactly (k) lines of (LL) passing below (v). The complexity (the maximum size) of the (k)-level in a line arrangement has been widely studied. In 1998 Dey proved an upper bound of (O(ncdot (k+1)^{1/3})). Due to the correspondence between lines in the plane and great-circles on the sphere, the asymptotic bounds carry over to arrangements of great-circles on the sphere, where the (k)-level denotes the vertices at distance (k) to a marked cell, the south pole.We prove an upper bound of (O((k+1)^2)) on the expected complexity of the ((le k))-level in great-circle arrangements if the south pole is chosen uniformly at random among all cells.We also consider arrangements of great ((d-1))-spheres on the (d)-sphere (SS^d) which are orthogonal to a set of random points on (SS^d). In this model, we prove that the expected complexity of the (k)-level is of order (Theta((k+1)^{d-1})).In both scenarios, our bounds are independent of $n$, showing that the distribution of arrangements under our sampling methods differs significantly from other methods studied in the literature, where the bounds do depend on $n$." @default.
- W3106683722 created "2020-12-07" @default.
- W3106683722 creator A5000735637 @default.
- W3106683722 creator A5005468020 @default.
- W3106683722 creator A5032317194 @default.
- W3106683722 creator A5048260458 @default.
- W3106683722 creator A5072926305 @default.
- W3106683722 creator A5078050536 @default.
- W3106683722 date "2020-10-09" @default.
- W3106683722 modified "2023-09-23" @default.
- W3106683722 title "On the average complexity of the $k$-level" @default.
- W3106683722 doi "https://doi.org/10.20382/jocg.v11i1a19" @default.
- W3106683722 hasPublicationYear "2020" @default.
- W3106683722 type Work @default.
- W3106683722 sameAs 3106683722 @default.
- W3106683722 citedByCount "0" @default.
- W3106683722 crossrefType "journal-article" @default.
- W3106683722 hasAuthorship W3106683722A5000735637 @default.
- W3106683722 hasAuthorship W3106683722A5005468020 @default.
- W3106683722 hasAuthorship W3106683722A5032317194 @default.
- W3106683722 hasAuthorship W3106683722A5048260458 @default.
- W3106683722 hasAuthorship W3106683722A5072926305 @default.
- W3106683722 hasAuthorship W3106683722A5078050536 @default.
- W3106683722 hasConcept C10138342 @default.
- W3106683722 hasConcept C114614502 @default.
- W3106683722 hasConcept C129782007 @default.
- W3106683722 hasConcept C134306372 @default.
- W3106683722 hasConcept C162324750 @default.
- W3106683722 hasConcept C17825722 @default.
- W3106683722 hasConcept C182306322 @default.
- W3106683722 hasConcept C198352243 @default.
- W3106683722 hasConcept C2524010 @default.
- W3106683722 hasConcept C33923547 @default.
- W3106683722 hasConcept C77553402 @default.
- W3106683722 hasConceptScore W3106683722C10138342 @default.
- W3106683722 hasConceptScore W3106683722C114614502 @default.
- W3106683722 hasConceptScore W3106683722C129782007 @default.
- W3106683722 hasConceptScore W3106683722C134306372 @default.
- W3106683722 hasConceptScore W3106683722C162324750 @default.
- W3106683722 hasConceptScore W3106683722C17825722 @default.
- W3106683722 hasConceptScore W3106683722C182306322 @default.
- W3106683722 hasConceptScore W3106683722C198352243 @default.
- W3106683722 hasConceptScore W3106683722C2524010 @default.
- W3106683722 hasConceptScore W3106683722C33923547 @default.
- W3106683722 hasConceptScore W3106683722C77553402 @default.
- W3106683722 hasIssue "1" @default.
- W3106683722 hasLocation W31066837221 @default.
- W3106683722 hasOpenAccess W3106683722 @default.
- W3106683722 hasPrimaryLocation W31066837221 @default.
- W3106683722 hasRelatedWork W1729223836 @default.
- W3106683722 hasRelatedWork W1986004959 @default.
- W3106683722 hasRelatedWork W2018858611 @default.
- W3106683722 hasRelatedWork W2031385155 @default.
- W3106683722 hasRelatedWork W2155295887 @default.
- W3106683722 hasRelatedWork W2159658403 @default.
- W3106683722 hasRelatedWork W2271249378 @default.
- W3106683722 hasRelatedWork W2507610879 @default.
- W3106683722 hasRelatedWork W2752028650 @default.
- W3106683722 hasRelatedWork W2887187121 @default.
- W3106683722 hasRelatedWork W2892882511 @default.
- W3106683722 hasRelatedWork W2901427372 @default.
- W3106683722 hasRelatedWork W2922631448 @default.
- W3106683722 hasRelatedWork W2949196049 @default.
- W3106683722 hasRelatedWork W2949983487 @default.
- W3106683722 hasRelatedWork W2951488272 @default.
- W3106683722 hasRelatedWork W2962838183 @default.
- W3106683722 hasRelatedWork W2970023904 @default.
- W3106683722 hasRelatedWork W2985417056 @default.
- W3106683722 hasRelatedWork W2998011969 @default.
- W3106683722 hasVolume "11" @default.
- W3106683722 isParatext "false" @default.
- W3106683722 isRetracted "false" @default.
- W3106683722 magId "3106683722" @default.
- W3106683722 workType "article" @default.