Convex Lineability in Copula and Quasi-copula Sets

Convex Lineability in Copula and Quasi-copula Sets | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Convex Lineability in Copula and Quasi-copula Sets Enrique de Amo, Juan Fernández-Sánchez, David García-Fernández, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8833057/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract In this paper, we investigate several subsets of n-copulas and n-quasi-copulas from the perspective of convex-lineability and the recently introduced concept of convex-spaceability. Our purpose is to determine when such families contain extremely large algebraic structures, namely linearly independent sets of cardinality of the continuum whose convex hull, and in some cases a closed convex linearly independent subset, remain entirely inside the class under study. These include the families of asymmetric copulas, copulas with maximal asymmetric measure, and proper n-quasi-copulas, among others. In contrast, for several other natural classes of copulas we show that (maximal) convex lineability holds while convex spaceability remains an open problem. Mathematics Subject Classification (2010). Primary 60E05; Secondary 62H05. Copula convex-lineability convex-spaceability quasi-copula Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 28 Apr, 2026 Reviews received at journal 28 Apr, 2026 Reviewers agreed at journal 26 Feb, 2026 Reviewers invited by journal 26 Feb, 2026 Editor assigned by journal 26 Feb, 2026 Submission checks completed at journal 10 Feb, 2026 First submitted to journal 09 Feb, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8833057","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":597501441,"identity":"0ed96d50-3bea-4e7c-b20e-2266d1aa291c","order_by":0,"name":"Enrique de Amo","email":"","orcid":"","institution":"University of Almería","correspondingAuthor":false,"prefix":"","firstName":"Enrique","middleName":"","lastName":"de Amo","suffix":""},{"id":597501442,"identity":"71fe3444-f21d-4a77-83ac-c31bad31984f","order_by":1,"name":"Juan Fernández-Sánchez","email":"","orcid":"","institution":"University of Almería","correspondingAuthor":false,"prefix":"","firstName":"Juan","middleName":"","lastName":"Fernández-Sánchez","suffix":""},{"id":597501444,"identity":"f2492fce-8d13-43b5-851e-f735582cc839","order_by":2,"name":"David García-Fernández","email":"","orcid":"","institution":"University of Almería","correspondingAuthor":false,"prefix":"","firstName":"David","middleName":"","lastName":"García-Fernández","suffix":""},{"id":597501447,"identity":"3f2b649e-eb59-491f-9165-168b50abfc2d","order_by":3,"name":"Manuel Úbeda-Flores","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAApElEQVRIiWNgGAWjYFACHhCyYWBgJ1FLGgMDM4laDpOgRXdG7sEHb2rOJ/Y3MzA+/EGMFrMbecmGc47dTpxxmIHZmIc4LTlm0jxstxMbDjOwSRPlMKAW8988/84lzj/MwP6TSIflmDHzth1I3AC0hYE4h515lyw5ty/ZeONhxmZp4rQczz344c03O9l5x5sPfiTKYUiAsYFEDaNgFIyCUTAKcAIA4B4yvP+o/d0AAAAASUVORK5CYII=","orcid":"","institution":"University of Almería","correspondingAuthor":true,"prefix":"","firstName":"Manuel","middleName":"","lastName":"Úbeda-Flores","suffix":""}],"badges":[],"createdAt":"2026-02-09 17:23:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8833057/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8833057/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103808302,"identity":"f0a9d5de-5a58-44e8-b6fb-69702176d2f7","added_by":"auto","created_at":"2026-03-03 07:42:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":402559,"visible":true,"origin":"","legend":"","description":"","filename":"ConvexlineabilityMediterranean.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8833057/v1_covered_66b10bb5-dcc1-4e48-8a32-73c78e413fa0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Convex Lineability in Copula and Quasi-copula Sets","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"mediterranean-journal-of-mathematics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mjom","sideBox":"Learn more about [Mediterranean Journal of Mathematics](http://link.springer.com/journal/9)","snPcode":"9","submissionUrl":"https://submission.nature.com/new-submission/9/3","title":"Mediterranean Journal of Mathematics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Copula, convex-lineability, convex-spaceability, quasi-copula","lastPublishedDoi":"10.21203/rs.3.rs-8833057/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8833057/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we investigate several subsets of n-copulas and n-quasi-copulas from the perspective of convex-lineability and the recently introduced concept of convex-spaceability. Our purpose is to determine when such families contain extremely large algebraic structures, namely linearly independent sets of cardinality of the continuum whose convex hull, and in some cases a closed convex linearly independent subset, remain entirely inside the class under study. These include the families of asymmetric copulas, copulas with maximal asymmetric measure, and proper n-quasi-copulas, among others. In contrast, for several other natural classes of copulas we show that (maximal) convex lineability holds while convex spaceability remains an open problem.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMathematics Subject Classification (2010).\u003c/strong\u003e Primary 60E05; Secondary 62H05.\u003c/p\u003e","manuscriptTitle":"Convex Lineability in Copula and Quasi-copula Sets","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-03 07:41:26","doi":"10.21203/rs.3.rs-8833057/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-28T08:07:58+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-28T08:03:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"3458218917009170165823385932296437312","date":"2026-02-26T11:08:56+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-26T09:57:48+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-26T09:33:36+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-10T11:26:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"Mediterranean Journal of Mathematics","date":"2026-02-09T17:08:22+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"mediterranean-journal-of-mathematics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mjom","sideBox":"Learn more about [Mediterranean Journal of Mathematics](http://link.springer.com/journal/9)","snPcode":"9","submissionUrl":"https://submission.nature.com/new-submission/9/3","title":"Mediterranean Journal of Mathematics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"1ca66da2-390d-4954-9efb-c1b7aef61a05","owner":[],"postedDate":"March 3rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-09T12:08:11+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-03 07:41:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8833057","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8833057","identity":"rs-8833057","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}