{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:13Z","timestamp":1753893853013,"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 sorting network is a shortest path from $12\\cdots n$ to $n\\cdots21$ in the Cayley graph of $S_n$ generated by nearest-neighbor swaps. For $m\\leq n$, consider the random $m$-particle sorting network obtained by choosing an $n$-particle sorting network uniformly at random and then observing only the relative order of $m$ particles chosen uniformly at random. We prove that the expected number of swaps in location $j$ in the subnetwork does not depend on $n$, and we provide a formula for it. Our proof is probabilistic, and involves a P\u00f3lya urn with non-integer numbers of balls. From the case $m=4$ we obtain a proof of a conjecture of Warrington. Our result is consistent with a conjectural limiting law of the subnetwork as $n\\to\\infty$ implied by the great circle conjecture of Angel, Holroyd, Romik and Vir\u00e1g.<\/jats:p>","DOI":"10.37236\/472","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:13:54Z","timestamp":1578698034000},"source":"Crossref","is-referenced-by-count":3,"title":["Random Subnetworks of Random Sorting Networks"],"prefix":"10.37236","volume":"17","author":[{"given":"Omer","family":"Angel","sequence":"first","affiliation":[]},{"given":"Alexander E.","family":"Holroyd","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,4,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:54:01Z","timestamp":1579287241000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1n23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/472","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,4,19]]},"article-number":"N23"}}