{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:37:20Z","timestamp":1787323040605,"version":"build-2736575974"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS1661063"],"award-info":[{"award-number":["DMS1661063"]}],"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":[[2022,9]]},"abstract":"<jats:p>We consider the rank of a class of sparse Boolean matrices of size $n \\times n$. In particular, we show that the probability that such a matrix has full rank, and is thus invertible, is a positive constant with value about 0.2574 for large $n$. The matrices arise as the vertex-edge incidence matrix of 1-out 3-uniform hypergraphs. The result that the null space is bounded in expectation can be contrasted with results for the usual models of sparse Boolean matrices, based on the vertex-edge incidence matrix of random $k$-uniform hypergraphs. For this latter model, the expected co-rank is linear in the number of vertices $n$, [A. Coja-Oghlan et al., in Proceedings of SODA, 2020, pp. 579--591], [C. Cooper, A. M. Frieze, and W. Pegden, in Proceedings of SODA, 2019, pp. 946--955]. For fields of higher order, the co-rank is typically Poisson distributed.<\/jats:p>","DOI":"10.1137\/21m1467572","type":"journal-article","created":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T10:06:50Z","timestamp":1663063610000},"page":"2238-2257","source":"Crossref","is-referenced-by-count":0,"title":["Rank of the Vertex-Edge Incidence Matrix of r-Out Hypergraphs"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5264-4401","authenticated-orcid":true,"given":"Colin","family":"Cooper","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8481-5615","authenticated-orcid":true,"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,9,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20494"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814068"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325708"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20272"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975994.35"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(200003)16:2<209::AID-RSA6>3.0.CO;2-1"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1002\/1098-2418(200010\/12)17:3\/4<197::AID-RSA2>3.0.CO;2-K"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975482.58"},{"key":"atypb9","volume-title":"Rank of the Vertex-Edge Incidence Matrix of $r$-Out Hypergraphs, https:\/\/arxiv.org\/pdf\/2107.05779.pdf","author":"Cooper C.","year":"2021"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579431"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(86)90077-8"},{"key":"atypb12","volume-title":"Introduction to Random Graphs","author":"Frieze A. M.","year":"2016"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1214\/14-AAP1060"},{"key":"atypb14","volume-title":"Naukova Dumka, Kyiv","author":"Kovalenko I. N.","year":"1986"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1467572","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:38:45Z","timestamp":1787319525000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1467572"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["10.1137\/21M1467572"],"URL":"https:\/\/doi.org\/10.1137\/21m1467572","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9]]}}}