{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:25:49Z","timestamp":1759335949813,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper we introduce a problem that bridges forbidden subposet and forbidden subconfiguration problems. The sets $F_1,F_2, \\dots,F_{|P|}$ form a copy\u00a0of a poset $P$, if there exists a bijection $i:P\\rightarrow \\{F_1,F_2, \\dots,F_{|P|}\\}$ such that for any $p,p'\\in P$ the relation $p&lt;_P p'$ implies $i(p)\\subsetneq i(p')$. A family $\\mathcal{F}$ of sets is $P$-free\u00a0if it does not contain any copy of $P$. The trace of a family $\\mathcal{F}$ on a set $X$ is $\\mathcal{F}|_X:=\\{F\\cap X: F\\in \\mathcal{F}\\}$.We introduce the following notions: $\\mathcal{F}\\subseteq 2^{[n]}$ is $l$-trace $P$-free\u00a0if for any $l$-subset $L\\subseteq [n]$, the family $\\mathcal{F}|_L$ is $P$-free and $\\mathcal{F}$ is trace $P$-free\u00a0if it is $l$-trace $P$-free for all $l\\le n$. As the first instances of these problems we determine the maximum size of trace $B$-free families, where $B$ is the butterfly poset on four elements $a,b,c,d$ with $a,b&lt;c,d$ and determine the asymptotics of \u00a0the maximum size of $(n-i)$-trace $K_{r,s}$-free families for $i=1,2$. We also propose a generalization of the main conjecture of the area of forbidden subposet problems.<\/jats:p>","DOI":"10.37236\/7073","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:10:03Z","timestamp":1578651003000},"source":"Crossref","is-referenced-by-count":2,"title":["Forbidden Subposet Problems for Traces of Set Families"],"prefix":"10.37236","volume":"25","author":[{"given":"D\u00e1niel","family":"Gerbner","sequence":"first","affiliation":[]},{"given":"Bal\u00e1zs","family":"Patk\u00f3s","sequence":"additional","affiliation":[]},{"given":"M\u00e1t\u00e9","family":"Vizer","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,9,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p49\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:26:06Z","timestamp":1579217166000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i3p49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,21]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7073","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,9,21]]},"article-number":"P3.49"}}