naa a22 4500 510736696 CHVBK 20180411083012.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s13366-012-0126-2 doi (NATIONALLICENCE)springer-10.1007/s13366-012-0126-2 Large simplices determined by finite point sets [Elektronische Daten] [Filip Morić, János Pach] Given a set P of n points in $$\mathbb R ^{d}$$ , let $${d}_{1}>d_{2}>\cdots $$ denote all distinct inter-point distances generated by point pairs in $$P$$ . It was shown by Schur, Martini, Perles, and Kupitz that there is at most one d-dimensional regular simplex of edge length $${d}_{1}$$ whose every vertex belongs to P. We extend this result by showing that for any k the number of d-dimensional regular simplices of edge length $${d}_{k}$$ generated by the points of P is bounded from above by a constant that depends only on d and k. The Managing Editors, 2012 Diameter graphs nationallicence Distance graphs nationallicence Large distances nationallicence Regular simplices nationallicence Number of cliques nationallicence Morić Filip Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland aut Pach János Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland aut Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 45-57 0138-4821 54:1<45 2013 54 13366 https://doi.org/10.1007/s13366-012-0126-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13366-012-0126-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Morić Filip Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland aut NATIONALLICENCE 700 1- Pach János Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland aut NATIONALLICENCE 773 0- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 45-57 0138-4821 54:1<45 2013 54 13366 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer