{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:28Z","timestamp":1753893868623,"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>Let $\\mathcal{G}$ be a properly face $2$-coloured (say black and white) piecewise-linear triangulation of the sphere with vertex set $V$. Consider the abelian group $\\mathcal{A}_W$ generated by the set $V$, with relations $r+c+s=0$ for all white triangles with vertices $r$, $c$ and $s$. The group $\\mathcal{A}_B$ can be defined similarly, using black triangles. These groups are related in the following manner $\\mathcal{A}_W\\cong\\mathcal{A}_B\\cong\\mathbb{Z}\\oplus\\mathbb{Z}\\oplus\\mathcal{C}$ where $\\mathcal{C}$ is a finite abelian group.The finite torsion subgroup $\\mathcal{C}$ is referred to as the canonical group of the triangulation. Let $m_t$ be the maximal order of $\\mathcal{C}$ over all properly face 2-coloured spherical triangulations with $t$ triangles of each colour. By relating such a triangulation to certain directed Eulerian\u00a0spherical embeddings of digraphs whose abelian sand-pile groups are isomorphic to the triangulation's canonical group we provide improved upper and lower bounds for $\\lim \\sup_{t\\rightarrow\\infty}(m_t)^{1\/t}$.<\/jats:p>","DOI":"10.37236\/5410","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:33:34Z","timestamp":1578692014000},"source":"Crossref","is-referenced-by-count":0,"title":["Growth Rates of Groups associated with Face 2-Coloured Triangulations and Directed Eulerian Digraphs on the Sphere"],"prefix":"10.37236","volume":"23","author":[{"given":"Thomas A.","family":"McCourt","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,3,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:30:49Z","timestamp":1579239049000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/5410","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,3,18]]},"article-number":"P1.51"}}