{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T09:04:43Z","timestamp":1774947883694,"version":"3.50.1"},"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>We show for $k \\geq 2$ that if $q\\geq 3$ and $n \\geq 2k+1$, or $q=2$ and $n \\geq 2k+2$, then any intersecting family ${\\cal F}$ of $k$-subspaces of an $n$-dimensional vector space over $GF(q)$ with $\\bigcap_{F \\in {\\cal F}} F=0$ has size at most $\\left[{n-1\\atop k-1}\\right]-q^{k(k-1)}\\left[{n-k-1\\atop k-1}\\right]+q^k$.  This bound is sharp as is shown by Hilton-Milner type families.  As an application of this result, we determine the chromatic number of the corresponding $q$-Kneser graphs.<\/jats:p>","DOI":"10.37236\/343","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:13:28Z","timestamp":1578698008000},"source":"Crossref","is-referenced-by-count":37,"title":["A Hilton-Milner Theorem for Vector Spaces"],"prefix":"10.37236","volume":"17","author":[{"given":"A.","family":"Blokhuis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. E.","family":"Brouwer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Chowdhury","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Frankl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Mussche","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Patk\u00f3s","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Sz\u0151nyi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2010,5,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r71\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r71\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:53:40Z","timestamp":1579287220000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r71"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,5,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/343","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,5,14]]},"article-number":"R71"}}