{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:02Z","timestamp":1753893842485,"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>In rotor-router aggregation on the square lattice $\\mathbb{Z}^2$, particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site.  The limiting shape of the cluster of occupied sites is a disk.  We consider a small change to the routing mechanism for sites on the $x$- and $y$-axes, resulting in a limiting shape which is a diamond instead of a disk.  We show that for a certain choice of initial rotors, the occupied cluster grows as a perfect diamond.<\/jats:p>","DOI":"10.37236\/424","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:59:33Z","timestamp":1578715173000},"source":"Crossref","is-referenced-by-count":6,"title":["Rotor-Router Aggregation on the Layered Square Lattice"],"prefix":"10.37236","volume":"17","author":[{"given":"Wouter","family":"Kager","sequence":"first","affiliation":[]},{"given":"Lionel","family":"Levine","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,11,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r152\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r152\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:22:04Z","timestamp":1579303324000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r152"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/424","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,11,5]]},"article-number":"R152"}}