We call a piecewise linear mapping from a planar triangulation to the plane a convex combination mapping<\/italic> if the image of every interior vertex is a convex combination of the images of its neighbouring vertices. Such mappings satisfy a discrete maximum principle and we show that they are one-to-one if they map the boundary of the triangulation homeomorphically to a convex polygon. This result can be viewed as a discrete version of the Rad\u00f3-Kneser-Choquet theorem for harmonic mappings, but is also closely related to Tutte\u2019s theorem on barycentric mappings of planar graphs.<\/p>","DOI":"10.1090\/s0025-5718-02-01466-7","type":"journal-article","created":{"date-parts":[[2003,2,10]],"date-time":"2003-02-10T16:10:52Z","timestamp":1044893452000},"page":"685-696","source":"Crossref","is-referenced-by-count":103,"title":["One-to-one piecewise linear mappings over triangulations"],"prefix":"10.1090","volume":"72","author":[{"given":"Michael","family":"Floater","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2002,10,17]]},"reference":[{"key":"1","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07233-2","volume-title":"Finite elements","author":"Braess, Dietrich","year":"1997","ISBN":"http:\/\/id.crossref.org\/isbn\/0521581877"},{"key":"2","series-title":"Frontiers in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971019","volume-title":"Mathematical aspects of numerical grid generation","volume":"8","year":"1991","ISBN":"http:\/\/id.crossref.org\/isbn\/089871267X"},{"key":"3","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1017\/S0370164600012281","article-title":"On the reciprocation of certain matrices","volume":"59","author":"Collar, A. 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