{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,6]],"date-time":"2024-04-06T05:18:08Z","timestamp":1712380688996},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"Let us consider a $3$-numerical semigroup $S=\\langle{a,b,N}\\rangle$. Given $m\\in S$, the triple $(x,y,z)\\in\\mathbb{N}^3$ is a factorization of $m$ in $S$ if $xa+yb+zN=m$. This work is focused on finding the full set of factorizations of any $m\\in S$ and as an application we compute the catenary degree of $S$. To this end, we relate a 2D tessellation to $S$ and we use it as a main tool.<\/jats:p>","DOI":"10.37236\/410","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:00:23Z","timestamp":1578697223000},"source":"Crossref","is-referenced-by-count":10,"title":["Factoring in Embedding Dimension Three Numerical Semigroups"],"prefix":"10.37236","volume":"17","author":[{"given":"F.","family":"Aguil\u00f3-Gost","sequence":"first","affiliation":[]},{"given":"P. A.","family":"Garc\u00eda-S\u00e1nchez","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,10,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r138\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r138\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:22:53Z","timestamp":1579285373000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r138"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/410","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10,15]]}}}