{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:06Z","timestamp":1753893846221,"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>Let $\\mathcal{F}$ be a finite family of axis-parallel boxes in $\\mathbb{R}^d$ such that $\\mathcal{F}$ contains no $k+1$ pairwise disjoint boxes.\u00a0We prove that if $\\mathcal{F}$ contains a subfamily $\\mathcal{M}$ of $k$ pairwise disjoint boxes with the property that for every $F\\in \\mathcal{F}$ and $M\\in \\mathcal{M}$ with $F \\cap M \\neq \\emptyset$, either $F$ contains a corner of $M$ or $M$ contains $2^{d-1}$ corners of $F$, then $\\mathcal{F}$ can be pierced by $O(k)$ points. One consequence of this result is that if $d=2$ and the ratio between any of the side lengths of any box is bounded by a constant, then $\\mathcal{F}$ can be pierced by $O(k)$ points. We further show that if for each two intersecting boxes in $\\mathcal{F}$ a corner of one is contained in the other, then $\\mathcal{F}$ can be pierced by at most $O(k\\log\\log(k))$ points, and in the special case where $\\mathcal{F}$ contains only cubes this bound improves to $O(k)$.<\/jats:p>","DOI":"10.37236\/7034","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:35:40Z","timestamp":1578670540000},"source":"Crossref","is-referenced-by-count":4,"title":["Piercing Axis-Parallel Boxes"],"prefix":"10.37236","volume":"25","author":[{"given":"Maria","family":"Chudnovsky","sequence":"first","affiliation":[]},{"given":"Sophie","family":"Spirkl","sequence":"additional","affiliation":[]},{"given":"Shira","family":"Zerbib","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,3,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p70\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p70\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:37:03Z","timestamp":1579235823000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p70"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7034","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,3,29]]},"article-number":"P1.70"}}