{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:50:57Z","timestamp":1759942257064,"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>For any finite Coxeter group $W$ of rank $n$ we show that the order complex of the lattice of non-crossing partitions $\\mathrm{NC}(W)$ embeds as a chamber subcomplex into a spherical building of type $A_{n-1}$.\u00a0We use this to give a new proof of the fact that the non-crossing partition lattice in type $A_n$ is supersolvable for all $n$. Moreover, we show that in case $B_n$, this is only the case if $n&lt;4$.\u00a0We also obtain a lower bound on the radius of the Hurwitz graph $H(W)$ in all types and re-prove that in type $A_n$ the radius is $\\binom{n}{2}$.\u00a0A Corrigendum for this paper was added on May 17, 2018.<\/jats:p>","DOI":"10.37236\/7200","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:37:55Z","timestamp":1578670675000},"source":"Crossref","is-referenced-by-count":0,"title":["Generalized Non-Crossing Partitions and Buildings"],"prefix":"10.37236","volume":"25","author":[{"given":"Julia","family":"Heller","sequence":"first","affiliation":[]},{"given":"Petra","family":"Schwer","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,2,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:38:37Z","timestamp":1579235917000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7200","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,2,16]]},"article-number":"P1.24"}}