Matches in SemOpenAlex for { <https://semopenalex.org/work/W2025334823> ?p ?o ?g. }
Showing items 1 to 57 of
57
with 100 items per page.
- W2025334823 abstract "(MATH) Rigid frameworks in some Euclidian space are embedded graphs having a unique local realization (up to Euclidian motions) for the given edge lengths, although globally they may have several. We study first the number of distinct planar embeddings of rigid graphs with n vertices. We show that, modulo planar rigid motions, this number is at most $2n-4choose n-2 approx 4n. We also exhibit several families which realize lower bounds of the order of 2n, 2.21n and 2.88n.(MATH) For the upper bound we use techniques from complex algebraic geometry, based on the (projective) Cayley-Menger variety CM 2,n(C)subset P_nchoose 2-1(C)$ over the complex numbers C. In this context, point configurations are represented by coordinates given by squared distances between all pairs of points. Sectioning the variety with 2n-4 hyperplanes yields at most deg(CM 2,n) zero-dimensional components, and one finds this degree to be D 2,n =frac122n-4choose n-2$. The lower bounds are related to inductive constructions of minimally rigid graphs via Henneberg sequences.(MATH) The same approach works in higher dimensions. In particular we show that it leads to an upper bound of 2 D^3,n= frac2^n-3n-2n-6choosen-3$ for the number of spatial embeddings with generic edge lengths of the $1$-skeleton of a simplicial polyhedron, up to rigid motions." @default.
- W2025334823 created "2016-06-24" @default.
- W2025334823 creator A5008565320 @default.
- W2025334823 creator A5055947023 @default.
- W2025334823 date "2002-06-05" @default.
- W2025334823 modified "2023-09-26" @default.
- W2025334823 title "On the number of embeddings of minimally rigid graphs" @default.
- W2025334823 cites W133608936 @default.
- W2025334823 cites W1970095165 @default.
- W2025334823 cites W1977438424 @default.
- W2025334823 cites W1987075624 @default.
- W2025334823 cites W1991581432 @default.
- W2025334823 cites W2041204798 @default.
- W2025334823 cites W2139834426 @default.
- W2025334823 cites W2158907148 @default.
- W2025334823 cites W2503612797 @default.
- W2025334823 cites W4250550876 @default.
- W2025334823 cites W4251345737 @default.
- W2025334823 cites W4251519580 @default.
- W2025334823 cites W62968843 @default.
- W2025334823 doi "https://doi.org/10.1145/513400.513404" @default.
- W2025334823 hasPublicationYear "2002" @default.
- W2025334823 type Work @default.
- W2025334823 sameAs 2025334823 @default.
- W2025334823 citedByCount "12" @default.
- W2025334823 countsByYear W20253348232012 @default.
- W2025334823 countsByYear W20253348232014 @default.
- W2025334823 countsByYear W20253348232020 @default.
- W2025334823 crossrefType "proceedings-article" @default.
- W2025334823 hasAuthorship W2025334823A5008565320 @default.
- W2025334823 hasAuthorship W2025334823A5055947023 @default.
- W2025334823 hasBestOaLocation W20253348232 @default.
- W2025334823 hasConcept C114614502 @default.
- W2025334823 hasConcept C33923547 @default.
- W2025334823 hasConcept C41008148 @default.
- W2025334823 hasConceptScore W2025334823C114614502 @default.
- W2025334823 hasConceptScore W2025334823C33923547 @default.
- W2025334823 hasConceptScore W2025334823C41008148 @default.
- W2025334823 hasLocation W20253348231 @default.
- W2025334823 hasLocation W20253348232 @default.
- W2025334823 hasLocation W20253348233 @default.
- W2025334823 hasOpenAccess W2025334823 @default.
- W2025334823 hasPrimaryLocation W20253348231 @default.
- W2025334823 hasRelatedWork W1974891317 @default.
- W2025334823 hasRelatedWork W1978042415 @default.
- W2025334823 hasRelatedWork W2017331178 @default.
- W2025334823 hasRelatedWork W2044189972 @default.
- W2025334823 hasRelatedWork W2260035625 @default.
- W2025334823 hasRelatedWork W2748952813 @default.
- W2025334823 hasRelatedWork W2899084033 @default.
- W2025334823 hasRelatedWork W2913765211 @default.
- W2025334823 hasRelatedWork W2976797620 @default.
- W2025334823 hasRelatedWork W3086542228 @default.
- W2025334823 isParatext "false" @default.
- W2025334823 isRetracted "false" @default.
- W2025334823 magId "2025334823" @default.
- W2025334823 workType "article" @default.