Matches in SemOpenAlex for { <https://semopenalex.org/work/W4226381519> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W4226381519 abstract "For integers $d geq 2$ and $k geq d+1$, a $k$-hole in a set $S$ of points in general position in $mathbb{R}^d$ is a $k$-tuple of points from $S$ in convex position such that the interior of their convex hull does not contain any point from $S$. For a convex body $K subseteq mathbb{R}^d$ of unit $d$-dimensional volume, we study the expected number $EH^K_{d,k}(n)$ of $k$-holes in a set of $n$ points drawn uniformly and independently at random from $K$. We prove an asymptotically tight lower bound on $EH^K_{d,k}(n)$ by showing that, for all fixed integers $d geq 2$ and $kgeq d+1$, the number $EH_{d,k}^K(n)$ is at least $Omega(n^d)$. For some small holes, we even determine the leading constant $lim_{n to infty}n^{-d}EH^K_{d,k}(n)$ exactly. We improve the currently best known lower bound on $lim_{n to infty}n^{-d}EH^K_{d,d+1}(n)$ by Reitzner and Temesvari (2019). In the plane, we show that the constant $lim_{n to infty}n^{-2}EH^K_{2,k}(n)$ is independent of $K$ for every fixed $k geq 3$ and we compute it exactly for $k=4$, improving earlier estimates by Fabila-Monroy, Huemer, and Mitsche (2015) and by the authors (2020)." @default.
- W4226381519 created "2022-05-05" @default.
- W4226381519 creator A5049492592 @default.
- W4226381519 creator A5072926305 @default.
- W4226381519 creator A5078050536 @default.
- W4226381519 date "2021-11-24" @default.
- W4226381519 modified "2023-09-26" @default.
- W4226381519 title "Tight bounds on the expected number of holes in random point sets" @default.
- W4226381519 doi "https://doi.org/10.48550/arxiv.2111.12533" @default.
- W4226381519 hasPublicationYear "2021" @default.
- W4226381519 type Work @default.
- W4226381519 citedByCount "0" @default.
- W4226381519 crossrefType "posted-content" @default.
- W4226381519 hasAuthorship W4226381519A5049492592 @default.
- W4226381519 hasAuthorship W4226381519A5072926305 @default.
- W4226381519 hasAuthorship W4226381519A5078050536 @default.
- W4226381519 hasBestOaLocation W42263815191 @default.
- W4226381519 hasConcept C112680207 @default.
- W4226381519 hasConcept C114614502 @default.
- W4226381519 hasConcept C121332964 @default.
- W4226381519 hasConcept C122637931 @default.
- W4226381519 hasConcept C134306372 @default.
- W4226381519 hasConcept C134912446 @default.
- W4226381519 hasConcept C145420912 @default.
- W4226381519 hasConcept C150397156 @default.
- W4226381519 hasConcept C199360897 @default.
- W4226381519 hasConcept C206194317 @default.
- W4226381519 hasConcept C2524010 @default.
- W4226381519 hasConcept C2777027219 @default.
- W4226381519 hasConcept C2779557605 @default.
- W4226381519 hasConcept C33923547 @default.
- W4226381519 hasConcept C41008148 @default.
- W4226381519 hasConcept C62520636 @default.
- W4226381519 hasConcept C77553402 @default.
- W4226381519 hasConceptScore W4226381519C112680207 @default.
- W4226381519 hasConceptScore W4226381519C114614502 @default.
- W4226381519 hasConceptScore W4226381519C121332964 @default.
- W4226381519 hasConceptScore W4226381519C122637931 @default.
- W4226381519 hasConceptScore W4226381519C134306372 @default.
- W4226381519 hasConceptScore W4226381519C134912446 @default.
- W4226381519 hasConceptScore W4226381519C145420912 @default.
- W4226381519 hasConceptScore W4226381519C150397156 @default.
- W4226381519 hasConceptScore W4226381519C199360897 @default.
- W4226381519 hasConceptScore W4226381519C206194317 @default.
- W4226381519 hasConceptScore W4226381519C2524010 @default.
- W4226381519 hasConceptScore W4226381519C2777027219 @default.
- W4226381519 hasConceptScore W4226381519C2779557605 @default.
- W4226381519 hasConceptScore W4226381519C33923547 @default.
- W4226381519 hasConceptScore W4226381519C41008148 @default.
- W4226381519 hasConceptScore W4226381519C62520636 @default.
- W4226381519 hasConceptScore W4226381519C77553402 @default.
- W4226381519 hasLocation W42263815191 @default.
- W4226381519 hasOpenAccess W4226381519 @default.
- W4226381519 hasPrimaryLocation W42263815191 @default.
- W4226381519 hasRelatedWork W1763880239 @default.
- W4226381519 hasRelatedWork W2012104218 @default.
- W4226381519 hasRelatedWork W2088414519 @default.
- W4226381519 hasRelatedWork W2890470282 @default.
- W4226381519 hasRelatedWork W2951276066 @default.
- W4226381519 hasRelatedWork W3126820753 @default.
- W4226381519 hasRelatedWork W4210739075 @default.
- W4226381519 hasRelatedWork W4287332066 @default.
- W4226381519 hasRelatedWork W4300128383 @default.
- W4226381519 hasRelatedWork W4300856049 @default.
- W4226381519 isParatext "false" @default.
- W4226381519 isRetracted "false" @default.
- W4226381519 workType "article" @default.