{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:24Z","timestamp":1753893804281,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The shadow of a collection   ${\\cal A}$ of $k$-sets  is defined as the collection of the $(k-1)$-sets which are contained in at least one $k$-set of  ${\\cal A}$. Given $|{\\cal A}|$, the size of the shadow is minimum  when ${\\cal A}$ is the family of the first $k$-sets in  squashed order  (by definition, a $k$-set $A$ is smaller than a $k$-set $B$ in the squashed order if the largest element of the symmetric difference of $A$ and $B$ is in $B$). We give a tight upper bound and an asymptotic formula  for the size of the shadow of squashed families of $k$-sets.<\/jats:p>","DOI":"10.37236\/1210","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:25:51Z","timestamp":1578705951000},"source":"Crossref","is-referenced-by-count":0,"title":["On the shadow of squashed families of $k$-sets"],"prefix":"10.37236","volume":"2","author":[{"given":"Fr\u00e9d\u00e9ric","family":"Maire","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1995,8,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:26:29Z","timestamp":1579328789000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v2i1r16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,8,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1995,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1210","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1995,8,25]]},"article-number":"R16"}}