{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:22:22Z","timestamp":1763468542438,"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>A set of permutations ${\\cal F} \\subseteq S_n$ is min-wise independent if for any set $X \\subseteq [n]$ and any $x \\in X$, when  $\\pi$ is chosen at random in ${\\cal F}$ we have ${\\bf P} \\left(\\min\\{\\pi(X)\\} = \\pi(x)\\right) = {{1}\\over {|X|}}$. This notion was introduced by Broder, Charikar, Frieze and Mitzenmacher and is motivated by an algorithm for filtering near-duplicate web documents. Linear permutations are an important class of permutations. Let $p$ be a (large) prime and let ${\\cal F}_p=\\{p_{a,b}:\\;1\\leq a\\leq p-1,\\,0\\leq b\\leq p-1\\}$ where for $x\\in [p]=\\{0,1,\\ldots,p-1\\}$, $p_{a,b}(x)=ax+b\\pmod p$. For $X\\subseteq [p]$ we let $F(X)=\\max_{x\\in X}\\left\\{{\\bf P}_{a,b}(\\min\\{p(X)\\}=p(x))\\right\\}$ where ${\\bf P}_{a,b}$ is over $p$ chosen uniformly at random from ${\\cal F}_p$. We show that as $k,p \\to\\infty$, ${\\bf E}_X[F(X)]={{1}\\over {k}}+O\\left({(\\log k)^3}\\over {k^{3\/2}}\\right)$ confirming that a simply chosen random linear permutation will suffice for an average set from the point of view of approximate min-wise independence.<\/jats:p>","DOI":"10.37236\/1504","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:04:50Z","timestamp":1578690290000},"source":"Crossref","is-referenced-by-count":14,"title":["Min-Wise Independent Linear Permutations"],"prefix":"10.37236","volume":"7","author":[{"given":"Tom","family":"Bohman","sequence":"first","affiliation":[]},{"given":"Colin","family":"Cooper","sequence":"additional","affiliation":[]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,4,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r26\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:23:37Z","timestamp":1579307017000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,4,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1504","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,4,23]]},"article-number":"R26"}}