{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T16:43:32Z","timestamp":1649177012095},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":5309,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1994,3]]},"abstract":"<jats:p>A Steiner quadruple system <jats:italic>SQS<\/jats:italic>(<jats:italic>v<\/jats:italic>) of order <jats:italic>v<\/jats:italic> is a family \u212c of 4-element subsets of a <jats:italic>v<\/jats:italic>-element set <jats:italic>V<\/jats:italic> such that each 3-element subset of <jats:italic>V<\/jats:italic> is contained in precisely one <jats:italic>B<\/jats:italic> \u2208 <jats:italic>\u212c<\/jats:italic>. We prove that if <jats:italic>T<\/jats:italic> \u2229 <jats:italic>B<\/jats:italic> \u2260 \u00f8 for all <jats:italic>B<\/jats:italic> \u2208 <jats:italic>\u212c<\/jats:italic> (i.e., if <jats:italic>T<\/jats:italic> is a <jats:italic>transversal<\/jats:italic>), then |<jats:italic>T<\/jats:italic>| \u2265 <jats:italic>v<\/jats:italic>\/2, and if <jats:italic>T<\/jats:italic> is a transversal of cardinality exactly <jats:italic>v<\/jats:italic>\/2, then <jats:italic>V \\ T<\/jats:italic> is a transversal as well (i.e., <jats:italic>T<\/jats:italic> is a <jats:italic>blocking set<\/jats:italic>). Also, in respect of the so-called \u2018doubling construction\u2019 that produces <jats:italic>SQS<\/jats:italic>(2<jats:italic>v<\/jats:italic>) from two copies of <jats:italic>SQS<\/jats:italic>(<jats:italic>v<\/jats:italic>), we give a necessary and sufficient condition for this operation to yield a Steiner quadruple system with blocking sets.<\/jats:p>","DOI":"10.1017\/s0963548300000997","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T11:16:59Z","timestamp":1221218219000},"page":"77-86","source":"Crossref","is-referenced-by-count":1,"title":["Blocking Sets in <i>SQS<\/i>(2<i>v<\/i>)"],"prefix":"10.1017","volume":"3","author":[{"given":"Mario","family":"Gionfriddo","sequence":"first","affiliation":[]},{"given":"Salvatore","family":"Milici","sequence":"additional","affiliation":[]},{"given":"Zsolt","family":"Tuza","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S0963548300000997_ref005","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1960-013-3"},{"key":"S0963548300000997_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01222263"},{"key":"S0963548300000997_ref001","unstructured":"[1] Berardi L. and Beutelspacher A. (to appear) On blocking sets in some block designs."},{"key":"S0963548300000997_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70267-X"},{"key":"S0963548300000997_ref002","first-page":"393","article-title":"Non-isomorphic Steiner quadruple systems","volume":"23","author":"Doyen","year":"1971","journal-title":"Bull. Soc. Math. Belg."},{"key":"S0963548300000997_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(80)80009-6"},{"key":"S0963548300000997_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70235-8"},{"key":"S0963548300000997_ref007","volume-title":"Quaderno n. 3 Sem. Geom","author":"Tallini","year":"1983"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548300000997","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T19:09:14Z","timestamp":1557947354000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548300000997\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,3]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1994,3]]}},"alternative-id":["S0963548300000997"],"URL":"https:\/\/doi.org\/10.1017\/s0963548300000997","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,3]]}}}