Geodesic
Factoring in embedding dimension three numerical semigroups
The electronic journal of combinatorics, Tome 17 (2010)
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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.
DOI : 10.37236/410
Classification : 05C90, 11D07, 11D45, 11P21 
@article{10_37236_410,
     author = {F. Aguil\'o-Gost and P. A. Garc{\'\i}a-S\'anchez},
     title = {Factoring in embedding dimension three numerical semigroups},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/410},
     zbl = {1204.05094},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/410/}
}
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F. Aguiló-Gost; P. A. García-Sánchez. Factoring in embedding dimension three numerical semigroups. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/410

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