{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:24:36Z","timestamp":1775053476495,"version":"3.50.1"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":4303,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1996,12]]},"abstract":"<jats:p>Let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548300002121inline1\"\/> be the hypergraph whose points are the subsets <jats:italic>X<\/jats:italic> of [n] := {1,\u2026,<jats:italic>n<\/jats:italic>} with <jats:italic>l<\/jats:italic>\u2264 |<jats:italic>X<\/jats:italic>| \u2264 <jats:italic>u<\/jats:italic>, <jats:italic>l<\/jats:italic> &lt; <jats:italic>u<\/jats:italic>, and whose edges are intervals in the Boolean lattice of the form <jats:italic>I<\/jats:italic> = {<jats:italic>C<\/jats:italic> \u2286[<jats:italic>n<\/jats:italic>] : <jats:italic>X<\/jats:italic>\u2286<jats:italic>C<\/jats:italic>\u2286<jats:italic>Y<\/jats:italic>} where |<jats:italic>X<\/jats:italic>| = <jats:italic>l<\/jats:italic>, |<jats:italic>Y<\/jats:italic>| = <jats:italic>u<\/jats:italic>, <jats:italic>X<\/jats:italic> \u2286 <jats:italic>Y<\/jats:italic>.We study the matching number <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548300002121inline2\"\/> i.e. the the maximum number of pairwise disjoint edges, and the covering number <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548300002121inline3\"\/> i.e. the minimum number of points which cover all edges. We prove that max <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548300002121inline4\"\/> and that for every \u03b5 &gt; 0 the inequalities <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548300002121inline5\"\/> hold, where for the lower bounds we suppose that n is not too small. The corresponding fractional numbers can be determined exactly. Moreover, we show by construction that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548300002121inline6\"\/><\/jats:p>","DOI":"10.1017\/s0963548300002121","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T11:13:14Z","timestamp":1221217994000},"page":"373-384","source":"Crossref","is-referenced-by-count":28,"title":["Interval Packing and Covering in the Boolean Lattice"],"prefix":"10.1017","volume":"5","author":[{"given":"Konrad","family":"Engel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S0963548300002121_ref012","first-page":"479","article-title":"Applications of the set-pair method in extremal hypergraph theory","volume":"3","author":"Tuza","year":"1994","journal-title":"Bolyai Society Mathematical Studies"},{"key":"S0963548300002121_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(81)90140-0"},{"key":"S0963548300002121_ref003","unstructured":"[3] Bouchemakh I. and Engel K. (1994) The order-interval hypergraph of afinite poset and the K\u00f6nig property. Discrete Math. (to appear)."},{"key":"S0963548300002121_ref013","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1007\/BFb0026314","volume-title":"CSL '88, Proc. 2nd Workshop: Lecture Notes in Computer Science","volume":"385","author":"Voigt","year":"1988"},{"key":"S0963548300002121_ref005","first-page":"63","article-title":"Methods for asymptotic counting","volume":"32","author":"Kleitman","year":"1981","journal-title":"Congressus Numerantium"},{"key":"S0963548300002121_ref007","first-page":"45","volume-title":"Combinatorial surveys, Proc. 6th British Comb. Conf., Egham 1977","author":"Lov\u00e1sz","year":"1977"},{"key":"S0963548300002121_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01904851"},{"key":"S0963548300002121_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF01171114"},{"key":"S0963548300002121_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(75)90058-8"},{"key":"S0963548300002121_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF01788531"},{"key":"S0963548300002121_ref008","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300001280"},{"key":"S0963548300002121_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(88)90082-9"},{"key":"S0963548300002121_ref014","unstructured":"[14] Warnke I. (1994) Personal communication."},{"key":"S0963548300002121_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF00814408"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548300002121","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T19:44:36Z","timestamp":1557690276000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548300002121\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,12]]}},"alternative-id":["S0963548300002121"],"URL":"https:\/\/doi.org\/10.1017\/s0963548300002121","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,12]]}}}