{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:40:49Z","timestamp":1787323249233,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["PGSD3-489418-2016"],"award-info":[{"award-number":["PGSD3-489418-2016"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009193","name":"Marsden Fund","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100009193","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1500343"],"award-info":[{"award-number":["1500343"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>We consider matroids with the property that every subset of the ground set of size $t$ is contained in both an $\\ell$-element circuit and an $\\ell$-element cocircuit; we say that such a matroid has the $(t,\\ell)$-property. We show that for any positive integer $t$, there is a finite number of matroids with the $(t,\\ell)$-property for $\\ell&lt;2t$; however, matroids with the $(t,2t)$-property form an infinite family. We say a matroid is a $t$-spike if there is a partition of the ground set into pairs such that the union of any $t$ pairs is a circuit and a cocircuit. Our main result is that if a sufficiently large matroid has the $(t,2t)$-property, then it is a $t$-spike. Finally, we present some properties of $t$-spikes.<\/jats:p>","DOI":"10.1137\/18m1182255","type":"journal-article","created":{"date-parts":[[2019,2,21]],"date-time":"2019-02-21T10:38:17Z","timestamp":1550745497000},"page":"358-372","source":"Crossref","is-referenced-by-count":3,"title":["On a Generalization of Spikes"],"prefix":"10.1137","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1136-418X","authenticated-orcid":true,"given":"Nick","family":"Brettell","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rutger","family":"Campbell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Deborah","family":"Chun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kevin","family":"Grace","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Geoff","family":"Whittle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,2,21]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2007.05.004"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2008.05.002"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2013.02.001"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.2001.2082"},{"key":"atypb5","unstructured":"J. Miller,\n                      Matroids in which Every Pair of Elements Belongs to Both a 4-circuit and a 4-cocircuit\n                      , M.Sc. thesis, Victoria University of Wellington, Wellington, New Zealand, 2014."},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"J. Oxley,\n                      Matroid Theory\n                      , 2nd ed., Oxf. Grad. Texts Math. 21, Oxford University Press, Oxford, 2011.","DOI":"10.1093\/acprof:oso\/9780198566946.001.0001"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2018.12.005"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1996.0049"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-30.1.264"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579179"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1966-129-2"},{"key":"atypb12","unstructured":"A. Williams,\n                      Detachable Pairs in 3-Connected Matroids\n                      , Ph.D. thesis, Victoria University of Wellington, Wellington, New Zealand, 2015."}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1182255","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:50:39Z","timestamp":1787320239000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1182255"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1182255"],"URL":"https:\/\/doi.org\/10.1137\/18m1182255","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}