{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:31Z","timestamp":1753893811442,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We investigate the orientable genus of $G_n$, the cartesian product of $n$ triangles, with a particular attention paid to the two smallest unsolved cases $n=4$ and $5$. Using a lifting method we present a general construction of a low-genus embedding of $G_n$ using a low-genus embedding of $G_{n-1}$. Combining this method with a computer search and a careful analysis of face structure we show that $30\\le \\gamma(G_4) \\le 37$ and $133 \\le\\gamma(G_5) \\le 190$. Moreover, our computer search resulted in more than $1300$ non-isomorphic minimum-genus embeddings of $G_3$. We also introduce genus range of a group and (strong) symmetric genus range of a Cayley graph and of a group. The (strong) symmetric genus range of irredundant Cayley graphs of $Z_p^n$ is calculated for all odd primes $p$.<\/jats:p>","DOI":"10.37236\/2951","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T18:04:21Z","timestamp":1578679461000},"source":"Crossref","is-referenced-by-count":1,"title":["Genus of the Cartesian Product of Triangles."],"prefix":"10.37236","volume":"22","author":[{"given":"Michal","family":"Kotrb\u010d\u00edk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toma\u017e","family":"Pisanski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2015,10,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p2\/ZIP","content-type":"application\/zip","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:09:26Z","timestamp":1579237766000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,16]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/2951","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,10,16]]},"article-number":"P4.2"}}