{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,6]],"date-time":"2023-05-06T21:40:45Z","timestamp":1683409245154},"reference-count":25,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[2007,5,1]],"date-time":"2007-05-01T00:00:00Z","timestamp":1177977600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,8,22]],"date-time":"2013-08-22T00:00:00Z","timestamp":1377129600000},"content-version":"vor","delay-in-days":2305,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["European Journal of Combinatorics"],"published-print":{"date-parts":[[2007,5]]},"DOI":"10.1016\/j.ejc.2006.02.003","type":"journal-article","created":{"date-parts":[[2006,3,24]],"date-time":"2006-03-24T12:42:37Z","timestamp":1143204157000},"page":"1163-1179","source":"Crossref","is-referenced-by-count":1,"title":["Transitive actions of finite abelian groups of sup-norm isometries"],"prefix":"10.1016","volume":"28","author":[{"given":"Bas","family":"Lemmens","sequence":"first","affiliation":[]},{"given":"Michael","family":"Scheutzow","sequence":"additional","affiliation":[]},{"given":"Colin","family":"Sparrow","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"4","key":"10.1016\/j.ejc.2006.02.003_b1","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/BF00960065","article-title":"Nonlinear models of diffusion on a finite space","volume":"76","author":"Akcoglu","year":"1987","journal-title":"Probab. Theory Related Fields"},{"issue":"1","key":"10.1016\/j.ejc.2006.02.003_b2","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1017\/S0305004105008832","article-title":"Iteration of order preserving subhomogeneous maps on a cone","volume":"140","author":"Akian","year":"2006","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"10.1016\/j.ejc.2006.02.003_b3","doi-asserted-by":"crossref","first-page":"405","DOI":"10.2140\/pjm.1956.6.405","article-title":"Extension of uniformly continuous transformations and hyperconvex metric spaces","volume":"6","author":"Aronszajn","year":"1956","journal-title":"Pacific J. Math."},{"key":"10.1016\/j.ejc.2006.02.003_b4","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/S0195-6698(13)80131-X","article-title":"Isometric embeddings in \u2113p-spaces","volume":"11","author":"Ball","year":"1990","journal-title":"European J. Combin."},{"issue":"4","key":"10.1016\/j.ejc.2006.02.003_b5","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/BF02187853","article-title":"Alternative proof of Sine\u2019s theorem on the size of a regular polygon in Rk with the \u2113\u221e-metric","volume":"7","author":"Blokhuis","year":"1992","journal-title":"Discrete Comput. Geom."},{"key":"10.1016\/j.ejc.2006.02.003_b6","series-title":"Geometry of Cuts and Metrics","author":"Deza","year":"1997"},{"key":"10.1016\/j.ejc.2006.02.003_b7","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/BF01474158","article-title":"Les dimension d\u2019un ensemble abstrait","volume":"68","author":"Fr\u00e9chet","year":"1910","journal-title":"Math. Ann."},{"key":"10.1016\/j.ejc.2006.02.003_b8","series-title":"Topics in Dynamics and Ergodic Theory","first-page":"125","article-title":"Periodic points of nonexpansive maps: a survey","volume":"vol. 310","author":"Lemmens","year":"2003"},{"issue":"2","key":"10.1016\/j.ejc.2006.02.003_b9","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/S0019-3577(01)80025-2","article-title":"Lower and upper bounds for \u03c9-limit sets of nonexpansive maps","volume":"12","author":"Lemmens","year":"2001","journal-title":"Indag. Math. (N.S.)"},{"issue":"4","key":"10.1016\/j.ejc.2006.02.003_b10","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1007\/s00029-003-0342-6","article-title":"A characterization of the periods of periodic points of 1-norm nonexpansive maps","volume":"9","author":"Lemmens","year":"2003","journal-title":"Selecta Math. (N.S.)"},{"issue":"3","key":"10.1016\/j.ejc.2006.02.003_b11","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1017\/S0143385704000665","article-title":"On the dynamics of sup-norm nonexpansive maps","volume":"25","author":"Lemmens","year":"2005","journal-title":"Ergodic Theory Dynam. Systems"},{"key":"10.1016\/j.ejc.2006.02.003_b12","series-title":"Fixed Point Theory and Applications","first-page":"189","article-title":"On transitive and commutative finite groups of isometries","author":"Lyons","year":"1992"},{"key":"10.1016\/j.ejc.2006.02.003_b13","unstructured":"P. Martus, Asymptotic properties of nonstationary operator sequences in the nonlinear case, Ph.D. Thesis, Friedrich-Alexander Univ., Erlangen-N\u00fcrnberg, Germany, 1989"},{"key":"10.1016\/j.ejc.2006.02.003_b14","doi-asserted-by":"crossref","first-page":"721","DOI":"10.2307\/2371222","article-title":"New foundations of euclidean geometry","volume":"53","author":"Menger","year":"1931","journal-title":"Amer. J. Math."},{"issue":"3","key":"10.1016\/j.ejc.2006.02.003_b15","doi-asserted-by":"crossref","first-page":"523","DOI":"10.57262\/die\/1371571149","article-title":"Omega limit sets of nonexpansive maps: finiteness and cardinality estimates","volume":"3","author":"Nussbaum","year":"1990","journal-title":"Differential Integral Equations"},{"key":"10.1016\/j.ejc.2006.02.003_b16","unstructured":"R.D. Nussbaum, personal communication, 1998"},{"issue":"2","key":"10.1016\/j.ejc.2006.02.003_b17","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1112\/S0024610798006796","article-title":"Admissible arrays and a generalization of Perron\u2013Frobenius theory","volume":"58","author":"Nussbaum","year":"1998","journal-title":"J. London Math. Soc."},{"issue":"1","key":"10.1016\/j.ejc.2006.02.003_b18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s000290050028","article-title":"Periodic points of nonexpansive maps and nonlinear generalizations of the Perron\u2013Frobenius theory","volume":"4","author":"Nussbaum","year":"1998","journal-title":"Selecta Math. (N.S.)"},{"issue":"659","key":"10.1016\/j.ejc.2006.02.003_b19","first-page":"1","article-title":"Generalizations of the Perron\u2013Frobenius theorem for nonlinear maps","volume":"138","author":"Nussbaum","year":"1999","journal-title":"Mem. Amer. Math. Soc."},{"key":"10.1016\/j.ejc.2006.02.003_b20","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0195-6698(88)80029-5","article-title":"Periods of nonexpansive operators on finite l1-spaces","volume":"9","author":"Scheutzow","year":"1988","journal-title":"European J. Combin."},{"issue":"3","key":"10.1016\/j.ejc.2006.02.003_b21","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1090\/S0002-9947-1938-1501980-0","article-title":"Metric spaces and positive definite functions","volume":"44","author":"Schoenberg","year":"1938","journal-title":"Trans. Amer. Math. Soc."},{"issue":"2","key":"10.1016\/j.ejc.2006.02.003_b22","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1090\/S0002-9939-1990-0948156-X","article-title":"A nonlinear Perron\u2013Frobenius theorem","volume":"109","author":"Sine","year":"1990","journal-title":"Proc. Amer. Math. Soc."},{"key":"10.1016\/j.ejc.2006.02.003_b23","unstructured":"D. Weller, Hilbert\u2019s metric, part metric and self mappings of a cone, Ph.D. Thesis, Universit\u00e4t Bremen, Germany, 1987"},{"key":"10.1016\/j.ejc.2006.02.003_b24","series-title":"Embeddings and Extensions in Analysis","author":"Wells","year":"1975"},{"issue":"2","key":"10.1016\/j.ejc.2006.02.003_b25","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/0097-3165(86)90089-0","article-title":"Minimum dimension embedding of finite metric spaces","volume":"42","author":"Witsenhausen","year":"1986","journal-title":"J. Combin. Theory Ser. A"}],"container-title":["European Journal of Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S019566980600028X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S019566980600028X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,5,6]],"date-time":"2023-05-06T21:17:43Z","timestamp":1683407863000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S019566980600028X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,5]]}},"alternative-id":["S019566980600028X"],"URL":"https:\/\/doi.org\/10.1016\/j.ejc.2006.02.003","relation":{},"ISSN":["0195-6698"],"issn-type":[{"value":"0195-6698","type":"print"}],"subject":[],"published":{"date-parts":[[2007,5]]}}}