{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:40:01Z","timestamp":1787319601825,"version":"build-2736575974"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100009193","name":"Marsden Fund","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100009193","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Rutherford Foundation"},{"DOI":"10.13039\/100008414","name":"University of Canterbury","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008414","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>For integers [Formula: see text] and [Formula: see text] exceeding one, a matroid [Formula: see text] on [Formula: see text] elements is nearly [Formula: see text]- cyclic if there is a cyclic ordering [Formula: see text] of its ground set such that every [Formula: see text] consecutive elements of [Formula: see text] are contained in an [Formula: see text]-element circuit and every [Formula: see text] consecutive elements of [Formula: see text] are contained in a [Formula: see text]-element cocircuit. In the case [Formula: see text], nearly [Formula: see text]-cyclic matroids have been studied previously. In this paper, we show that if [Formula: see text] is nearly [Formula: see text]-cyclic and [Formula: see text] is sufficiently large, then these [Formula: see text]-element circuits and [Formula: see text]-element cocircuits are consecutive in [Formula: see text] in a prescribed way, that is, [Formula: see text] is \u201c[Formula: see text]-cyclic.\u201d Furthermore, we show that, given [Formula: see text] and [Formula: see text] where [Formula: see text], every [Formula: see text]-cyclic matroid on [Formula: see text] elements is a weak-map image of the [Formula: see text]th truncation of a certain [Formula: see text]-cyclic matroid. If [Formula: see text], this certain matroid is the rank-[Formula: see text] whirl, and if [Formula: see text], this certain matroid is the rank-[Formula: see text] free swirl.<\/jats:p>","DOI":"10.1137\/21m1468747","type":"journal-article","created":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T04:15:30Z","timestamp":1687320930000},"page":"1212-1236","source":"Crossref","is-referenced-by-count":1,"title":["Cyclic Matroids"],"prefix":"10.1137","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1136-418X","authenticated-orcid":true,"given":"Nick","family":"Brettell","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Charles","family":"Semple","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8902-484X","authenticated-orcid":true,"given":"Gerry","family":"Toft","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,6,21]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548306007942"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/18M1182255"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2019.06.002"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-10.37.26"},{"key":"ref5","unstructured":"J. Miller , Matroids in Which Every Pair of Elements Belongs to Both a 4-Circuit and a 4-Cocircuit, MSc thesis, Victoria University of Wellington, 2014."},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198566946.001.0001"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2018.12.005"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1966-129-2"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1468747","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:50:29Z","timestamp":1787316629000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1468747"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,21]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6,30]]}},"alternative-id":["10.1137\/21M1468747"],"URL":"https:\/\/doi.org\/10.1137\/21m1468747","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,21]]}}}