{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T00:35:28Z","timestamp":1759365328314,"version":"build-2065373602"},"reference-count":20,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[2003,5,1]],"date-time":"2003-05-01T00:00:00Z","timestamp":1051747200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2003,5,1]],"date-time":"2003-05-01T00:00:00Z","timestamp":1051747200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":3730,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Advances in Applied Mathematics"],"published-print":{"date-parts":[[2003,5]]},"DOI":"10.1016\/s0196-8858(02)00500-6","type":"journal-article","created":{"date-parts":[[2003,5,12]],"date-time":"2003-05-12T18:40:50Z","timestamp":1052764850000},"page":"591-606","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"title":["Unique representability and matroid reconstruction"],"prefix":"10.1016","volume":"30","author":[{"given":"William P.","family":"Miller","sequence":"first","affiliation":[]}],"member":"78","reference":[{"year":"1957","series-title":"Geometric Algebra","author":"Artin","key":"10.1016\/S0196-8858(02)00500-6_BIB001"},{"year":"1952","series-title":"Linear Algebra and Projective Geometry","author":"Baer","key":"10.1016\/S0196-8858(02)00500-6_BIB002"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB003","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/0095-8956(79)90056-X","article-title":"On Reid's characterization of the ternary matroids","volume":"26","author":"Bixby","year":"1979","journal-title":"J. Combin. Theory Ser. B"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB004","series-title":"Surveys in Combinatorics","first-page":"221","article-title":"A graph reconstructor's manual","volume":"166","author":"Bondy","year":"1991"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB005","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1006\/aama.1996.0018","article-title":"Matroids with no (q+2)-point line minors","volume":"17","author":"Bonin","year":"1996","journal-title":"Adv. in Appl. Math."},{"key":"10.1016\/S0196-8858(02)00500-6_BIB006","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1006\/eujc.1999.0245","article-title":"Characterizing combinatorial geometries by numerical invariants","volume":"20","author":"Bonin","year":"1999","journal-title":"European J. Combin."},{"key":"10.1016\/S0196-8858(02)00500-6_BIB007","series-title":"Graphs and Combinatorics","first-page":"226","article-title":"Reconstructing combinatorial geometries","volume":"406","author":"Brylawski","year":"1974"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB008","series-title":"Teorie Combinatorie, Proc. 1973 Internat. Colloq.","first-page":"83","article-title":"Uniquely representable combinatorial geometries","author":"Brylawski","year":"1976"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB009","series-title":"Matroid Applications","article-title":"The Tutte polynomial and its applications","author":"Brylawski","year":"1992"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB010","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1006\/jctb.2000.1963","article-title":"The excluded minors for GF(4)-representable matroids","volume":"79","author":"Geelen","year":"2000","journal-title":"J. Combin. Theory Ser. B."},{"key":"10.1016\/S0196-8858(02)00500-6_BIB011","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/0095-8956(87)90013-X","article-title":"Reconstructing graphs from their k-edge deleted subgraphs","volume":"43","author":"Godsil","year":"1987","journal-title":"J. Combin. Theory Ser. B."},{"year":"1979","series-title":"Projective Geometries Over Finite Fields","author":"Hirschfeld","key":"10.1016\/S0196-8858(02)00500-6_BIB012"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB013","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1112\/blms\/20.1.5","article-title":"On the uniqueness of matroid representations over GF(4)","volume":"20","author":"Kahn","year":"1988","journal-title":"Bull. London Math. Soc."},{"key":"10.1016\/S0196-8858(02)00500-6_BIB014","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0095-8956(72)90068-8","article-title":"A note on the line reconstruction problem","volume":"13","author":"Lov\u00e1sz","year":"1972","journal-title":"J. Combin. Theory Ser. B"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB015","unstructured":"W.P. Miller, Approaches to matroid reconstruction problems, PhD thesis, The George Washington University, 1995"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB016","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0012-365X(95)00227-N","article-title":"Techniques in matroid reconstruction","volume":"170","author":"Miller","year":"1997","journal-title":"Discrete Math."},{"key":"10.1016\/S0196-8858(02)00500-6_BIB017","series-title":"Selected Topics in Graph Theory","first-page":"205","article-title":"The reconstruction problem","author":"Nash-Williams","year":"1978"},{"year":"1992","series-title":"Matroid Theory","author":"Oxley","key":"10.1016\/S0196-8858(02)00500-6_BIB018"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB019","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0095-8956(79)90055-8","article-title":"Matroid representations over GF(3)","volume":"26","author":"Seymour","year":"1979","journal-title":"J. Combin. Theory Ser. B"},{"key":"10.1016\/S0196-8858(02)00500-6_BIB020","first-page":"144","article-title":"A homotopy theorem for matroids, I, II","volume":"88","author":"Tutte","year":"1958","journal-title":"Trans. Amer. Math. Soc."}],"container-title":["Advances in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0196885802005006?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0196885802005006?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T06:44:57Z","timestamp":1759301097000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0196885802005006"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2003,5]]}},"alternative-id":["S0196885802005006"],"URL":"https:\/\/doi.org\/10.1016\/s0196-8858(02)00500-6","relation":{},"ISSN":["0196-8858"],"issn-type":[{"type":"print","value":"0196-8858"}],"subject":[],"published":{"date-parts":[[2003,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Unique representability and matroid reconstruction","name":"articletitle","label":"Article Title"},{"value":"Advances in Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/S0196-8858(02)00500-6","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2003 Elsevier Science (USA). All rights reserved.","name":"copyright","label":"Copyright"}]}}