{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821487,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Inspired by the infinite families of finite and affine root systems, we define a \"stretching\" operation on general crystallographic root systems which, on the level of Coxeter diagrams, replaces a vertex with a path of unlabeled edges. We embed a root system into its stretched versions using a similar operation on individual roots. For a fixed root, we describe the long-term behavior of two associated structures as we lengthen the stretched path: the downset in the root poset and Reading's arrangement of shards. We show that both eventually admit a uniform description, and deduce enumerative consequences: the size of the downset is eventually a polynomial, and the number of shards grows exponentially.<\/jats:p>","DOI":"10.37236\/10029","type":"journal-article","created":{"date-parts":[[2021,8,13]],"date-time":"2021-08-13T01:28:11Z","timestamp":1628818091000},"source":"Crossref","is-referenced-by-count":0,"title":["Stability of Stretched Root Systems, Root Posets and Shards"],"prefix":"10.37236","volume":"28","author":[{"given":"Will","family":"Dana","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,8,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p38\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,13]],"date-time":"2021-08-13T01:28:11Z","timestamp":1628818091000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i3p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,13]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/10029","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,8,13]]},"article-number":"P3.38"}}