Construction of Balanced n-ary Designs via Complete Multiset Spaces

Construction of Balanced n-ary Designs via Complete Multiset Spaces | 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 Construction of Balanced n-ary Designs via Complete Multiset Spaces Sudesh Srivastav, Apurv Srivastav This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8595082/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We study balanced n-ary block designs that allow repeated treatments within blocks, motivated by applications in dose-response and repeated-measure experiments. We introduce a master (k+1)-ary design with explicit replication and pairwise concurrence parameters. Systematic symmetry-preserving deletions generate infinite families of lower-arity balanced designs, for which explicit formulas for replication numbers, structured expressions for pairwise concurrences, and the resulting information matrix under the fixed-effects model are obtained. These results establish a rigorous link between combinatorial Sv-symmetry and statistical optimality. Simulation studies show that the proposed multiset-based designs, by maintaining equireplication, yield lower contrast variances than random multiset arrangements with unequal replication numbers. Potential applications include doseresponse studies, resampling-based simulations, and repeated-measures experiments. AMS Subject Classification (2020): 62K10 · 05B05 Balanced n-ary design Multiset design Pairwise concurrence Information matrix Optimal design Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-8595082","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":625268671,"identity":"53358568-664b-4a8e-9564-22f0abd80613","order_by":0,"name":"Sudesh Srivastav","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYJCCA0Asx8DA3IDgEqPFmIeBkQQtIJDYQ7QW+f6zDw/z1NSl75dIbPxcUMEgx3cjAb8WgxvpBod5jh3O7ZFIbJaecYbBWJKgFgk2hoMz2A6AtDRI87YxJG4gpEW+/xhQy7+6dB6gLb95/zHUE9TCcCCN4cDHNuYEoJY2ad4GhgQDwn4Baek7bNhz5mGbNc8xCcOZZx4QdBjzh4RvdfLs7cmHb/PU2MjzHSfkMDQgQZryUTAKRsEoGAXYAQDWykXNvSPLKAAAAABJRU5ErkJggg==","orcid":"","institution":"Tulane University","correspondingAuthor":true,"prefix":"","firstName":"Sudesh","middleName":"","lastName":"Srivastav","suffix":""},{"id":625268672,"identity":"e7776809-0aa1-4e43-825d-7901f9ccd088","order_by":1,"name":"Apurv Srivastav","email":"","orcid":"","institution":"University of Delaware","correspondingAuthor":false,"prefix":"","firstName":"Apurv","middleName":"","lastName":"Srivastav","suffix":""}],"badges":[],"createdAt":"2026-01-13 18:53:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8595082/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8595082/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107704478,"identity":"c31d2498-cd42-456a-997d-9d13e113ceb9","added_by":"auto","created_at":"2026-04-24 08:45:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":288245,"visible":true,"origin":"","legend":"","description":"","filename":"sankhyafinal.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8595082/v1_covered_a162fad7-626f-4ea3-b4c3-3a41f85510ed.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Construction of Balanced n-ary Designs via Complete Multiset Spaces","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Balanced n-ary design, Multiset design, Pairwise concurrence, Information matrix, Optimal design","lastPublishedDoi":"10.21203/rs.3.rs-8595082/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8595082/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe study balanced n-ary block designs that allow repeated treatments within blocks, motivated by applications in dose-response and repeated-measure experiments. 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