Matches in SemOpenAlex for { <https://semopenalex.org/work/W2209321361> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W2209321361 abstract "Let $k,d,lambda geqslant 1$ be integers with $dgeqslant lambda $ and let $X$ be a finite set of points in $mathbb{R}^{d}$. A $(d-lambda)$-plane $L$ transversal to the convex hulls of all $k$-sets of $X$ is called Kneser transversal. If in addition $L$ contains $(d-lambda)+1$ points of $X$, then $L$ is called complete Kneser this http URL this paper, we present various results on the existence of (complete) Kneser transversals for $lambda =2,3$. In order to do this, we introduce the notions of stability and instability for (complete) Kneser transversals. We first give a stability result for collections of $d+2(k-lambda)$ points in $mathbb{R}^d$ with $k-lambdageqslant 2$ and $lambda =2,3$. We then present a description of Kneser transversals $L$ of collections of $d+2(k-lambda)$ points in $mathbb{R}^d$ with $k-lambdageqslant 2$ for $lambda =2,3$. We show that either $L$ is a complete Kneser transversal or it contains $d-2(lambda-1)$ points and the remaining $2(k-1)$ points of $X$ are matched in $k-1$ pairs in such a way that $L$ intersects the corresponding closed segments determined by them. The latter leads to new upper and lower bounds (in the case when $lambda =2$ and $3$) for $m(k,d,lambda)$ defined as the maximum positive integer $n$ such that every set of $n$ points (not necessarily in general position) in $mathbb{R}^{d}$ admit a Kneser transversal.Finally, by using oriented matroid machinery, we present some computational results (closely related to the stability and unstability notions). We determine the existence of (complete) Kneser transversals for each of the $246$ different order types of configurations of $7$ points in $mathbb{R}^3$." @default.
- W2209321361 created "2016-06-24" @default.
- W2209321361 creator A5047487492 @default.
- W2209321361 creator A5055119261 @default.
- W2209321361 creator A5063551926 @default.
- W2209321361 creator A5080195854 @default.
- W2209321361 date "2016-01-04" @default.
- W2209321361 modified "2023-09-30" @default.
- W2209321361 title "Codimension two and three Kneser Transversals" @default.
- W2209321361 cites W1927748389 @default.
- W2209321361 cites W1980414131 @default.
- W2209321361 cites W2003995429 @default.
- W2209321361 cites W2971330320 @default.
- W2209321361 hasPublicationYear "2016" @default.
- W2209321361 type Work @default.
- W2209321361 sameAs 2209321361 @default.
- W2209321361 citedByCount "0" @default.
- W2209321361 crossrefType "posted-content" @default.
- W2209321361 hasAuthorship W2209321361A5047487492 @default.
- W2209321361 hasAuthorship W2209321361A5055119261 @default.
- W2209321361 hasAuthorship W2209321361A5063551926 @default.
- W2209321361 hasAuthorship W2209321361A5080195854 @default.
- W2209321361 hasConcept C10138342 @default.
- W2209321361 hasConcept C112680207 @default.
- W2209321361 hasConcept C114614502 @default.
- W2209321361 hasConcept C120665830 @default.
- W2209321361 hasConcept C121332964 @default.
- W2209321361 hasConcept C134306372 @default.
- W2209321361 hasConcept C162324750 @default.
- W2209321361 hasConcept C182306322 @default.
- W2209321361 hasConcept C199360897 @default.
- W2209321361 hasConcept C2524010 @default.
- W2209321361 hasConcept C2778113609 @default.
- W2209321361 hasConcept C2780130068 @default.
- W2209321361 hasConcept C33923547 @default.
- W2209321361 hasConcept C41008148 @default.
- W2209321361 hasConcept C83979697 @default.
- W2209321361 hasConcept C97137487 @default.
- W2209321361 hasConceptScore W2209321361C10138342 @default.
- W2209321361 hasConceptScore W2209321361C112680207 @default.
- W2209321361 hasConceptScore W2209321361C114614502 @default.
- W2209321361 hasConceptScore W2209321361C120665830 @default.
- W2209321361 hasConceptScore W2209321361C121332964 @default.
- W2209321361 hasConceptScore W2209321361C134306372 @default.
- W2209321361 hasConceptScore W2209321361C162324750 @default.
- W2209321361 hasConceptScore W2209321361C182306322 @default.
- W2209321361 hasConceptScore W2209321361C199360897 @default.
- W2209321361 hasConceptScore W2209321361C2524010 @default.
- W2209321361 hasConceptScore W2209321361C2778113609 @default.
- W2209321361 hasConceptScore W2209321361C2780130068 @default.
- W2209321361 hasConceptScore W2209321361C33923547 @default.
- W2209321361 hasConceptScore W2209321361C41008148 @default.
- W2209321361 hasConceptScore W2209321361C83979697 @default.
- W2209321361 hasConceptScore W2209321361C97137487 @default.
- W2209321361 hasLocation W22093213611 @default.
- W2209321361 hasOpenAccess W2209321361 @default.
- W2209321361 hasPrimaryLocation W22093213611 @default.
- W2209321361 hasRelatedWork W1591659877 @default.
- W2209321361 hasRelatedWork W1983172787 @default.
- W2209321361 hasRelatedWork W2018531473 @default.
- W2209321361 hasRelatedWork W2026385148 @default.
- W2209321361 hasRelatedWork W2075929517 @default.
- W2209321361 hasRelatedWork W2095388396 @default.
- W2209321361 hasRelatedWork W2106229536 @default.
- W2209321361 hasRelatedWork W2256839718 @default.
- W2209321361 hasRelatedWork W2568178535 @default.
- W2209321361 hasRelatedWork W2760042202 @default.
- W2209321361 hasRelatedWork W2766204907 @default.
- W2209321361 hasRelatedWork W2772468309 @default.
- W2209321361 hasRelatedWork W2949297341 @default.
- W2209321361 hasRelatedWork W2949868240 @default.
- W2209321361 hasRelatedWork W2951503862 @default.
- W2209321361 hasRelatedWork W2954517359 @default.
- W2209321361 hasRelatedWork W3014789549 @default.
- W2209321361 hasRelatedWork W3121997785 @default.
- W2209321361 hasRelatedWork W3122675848 @default.
- W2209321361 hasRelatedWork W3130877181 @default.
- W2209321361 isParatext "false" @default.
- W2209321361 isRetracted "false" @default.
- W2209321361 magId "2209321361" @default.
- W2209321361 workType "article" @default.