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<title>GAP (NumericalSgps) - References</title>
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<p><a id="X7A6F98FD85F02BFE" name="X7A6F98FD85F02BFE"></a></p>
<h3>References</h3>
<p><a id="biBBF06" name="biBBF06"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">BF06</span>] <b class='Bib_author'>Barucci, V. and Fröberg, R.</b>,
<i class='Bib_title'>Associated graded rings of one-dimensional analytically
irreducible rings</i>,
<span class='Bib_journal'>J. Algebra</span>,
<em class='Bib_volume'>304</em>
(<span class='Bib_year'>2006</span>),
<span class='Bib_pages'>349--358</span>.
</p>
<p><a id="biBB-A08" name="biBB-A08"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">Bra08</span>] <b class='Bib_author'>Bras-Amor{\'o}s, M.</b>,
<i class='Bib_title'>Fibonacci-like behavior of the number of numerical semigroups of
a given genus</i>,
<span class='Bib_journal'>Semigroup Forum</span>,
<em class='Bib_volume'>76</em>
(<span class='Bib_year'>2008</span>),
<span class='Bib_pages'>379--384</span>.
</p>
<p><a id="biBRos05" name="biBRos05"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">BR08</span>] <b class='Bib_author'>Bullejos, M. and Rosales, J. C.</b>,
<i class='Bib_title'>Proportionally modular diophantine inequalities and the Stern-Brocot
tree</i>,
<span class='Bib_journal'>MATHEMATICS OF COMPUTATION</span>
(<span class='Bib_year'>2008</span>).
</p>
<p><a id="biBMR1283022" name="biBMR1283022"></a></p>
<p class='Bib_entry'>
[<span class='Bib_keyLink'><a href="http://www.ams.org/mathscinet-getitem?mr=MR1283022">CD94</a></span>] <b class='Bib_author'>Contejean, E. and Devie, H.</b>,
<i class='Bib_title'>An efficient incremental algorithm for solving systems of
linear Diophantine equations</i>,
<span class='Bib_journal'>Inform. and Comput.</span>,
<em class='Bib_volume'>113</em> (<span class='Bib_number'>1</span>)
(<span class='Bib_year'>1994</span>),
<span class='Bib_pages'>143--172</span>.
</p>
<p><a id="biBE01" name="biBE01"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">Eli01</span>] <b class='Bib_author'>Elias, J.</b>,
<i class='Bib_title'>On the deep structure of the blowing-up of curve
singularities</i>,
<span class='Bib_journal'>Math. Proc. Camb. Phil. Soc.</span>,
<em class='Bib_volume'>131</em>
(<span class='Bib_year'>2001</span>),
<span class='Bib_pages'>227--240</span>.
</p>
<p><a id="biBGHKb" name="biBGHKb"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">GH06</span>] <b class='Bib_author'>Geroldinger, A. and Halter-Koch, F.</b>,
<i class='Bib_title'>Non-unique Factorizations: Algebraic, Combinatorial and
Analytic Theory</i>,
<span class='Bib_publisher'>Chapman \& Hall/CRC</span>
(<span class='Bib_year'>2006</span>).
</p>
<p><a id="biBHS04" name="biBHS04"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">HS04a</span>] <b class='Bib_author'>Herzinger, K. and Sanford, R.</b>,
<i class='Bib_title'>Minimal Generating Sets for Relative Ideals in Numerical Semigroups
of Multiplicity Eight</i>,
<span class='Bib_journal'>Communications in Algebra</span>,
<em class='Bib_volume'>32</em> (<span class='Bib_number'>12</span>)
(<span class='Bib_year'>2004</span>),
<span class='Bib_pages'>4713-4731</span>.
</p>
<p><a id="biBHS04" name="biBHS04"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">HS04b</span>] <b class='Bib_author'>Herzinger, K. and Sanford, R.</b>,
<i class='Bib_title'>Minimal generating sets for relative ideals in numerical
semigroups of multiplicity eight</i>,
<span class='Bib_journal'>Comm. Algebra</span>,
<em class='Bib_volume'>32</em> (<span class='Bib_number'>12</span>)
(<span class='Bib_year'>2004</span>),
<span class='Bib_pages'>4713--4731</span>.
</p>
<p><a id="biBRGS04" name="biBRGS04"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">JCR04</span>] <b class='Bib_author'>J. C. Rosales, P. A. G.-S.</b>,
<i class='Bib_title'>Every positive integer is the Frobenius number
of an irreducible numerical semigroup with at most four generators</i>,
<span class='Bib_journal'>Ark. Mat.</span>,
<em class='Bib_volume'>42</em>
(<span class='Bib_year'>2004</span>),
<span class='Bib_pages'>301-306</span>.
</p>
<p><a id="biBRGGB03" name="biBRGGB03"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">GB03</span>] <b class='Bib_author'>J. C. Rosales P. A. Garc\'ia-S\'anchez, J. I. G.-G. and Branco, M. B.</b>,
<i class='Bib_title'>Numerical semigroups with maximal embedding dimension</i>,
<span class='Bib_journal'>J. Algebra</span>,
<em class='Bib_volume'>2</em>
(<span class='Bib_year'>2003</span>),
<span class='Bib_pages'>47--53</span>.
</p>
<p><a id="biBRGGB04" name="biBRGGB04"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">GB04</span>] <b class='Bib_author'>J. C. Rosales P. A. Garc\'ia-S\'anchez, J. I. G.-G. and Branco, M. B.</b>,
<i class='Bib_title'>Arf numerical semigroups</i>,
<span class='Bib_journal'>J. Algebra</span>,
<em class='Bib_volume'>276</em>
(<span class='Bib_year'>2004</span>),
<span class='Bib_pages'>3--12</span>.
</p>
<p><a id="biBRGGJ03" name="biBRGGJ03"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">GJ03</span>] <b class='Bib_author'>J. C. Rosales P. A. Garc\'ia-S\'anchez, J. I. G.-G. and Jiménez-Madrid, J. A.</b>,
<i class='Bib_title'>The oversemigroups of a numerical semigroup</i>,
<span class='Bib_journal'>Semigroup Forum</span>,
<em class='Bib_volume'>67</em>
(<span class='Bib_year'>2003</span>),
<span class='Bib_pages'>145-158</span>.
</p>
<p><a id="biBRGGJ04" name="biBRGGJ04"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">GM04</span>] <b class='Bib_author'>J. C. Rosales P. A. Garc\'ia-S\'anchez J. I. Garc\'ia-Garc\'ia, and Madrid, J. A. J.</b>,
<i class='Bib_title'>Fundamental gaps in numerical semigroups</i>,
<span class='Bib_journal'>J. Pure Appl. Algebra</span>,
<em class='Bib_volume'>189</em> (<span class='Bib_number'>1-3</span>)
(<span class='Bib_year'>2004</span>),
<span class='Bib_pages'>301--313</span>.
</p>
<p><a id="biBFGH87" name="biBFGH87"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">FH87</span>] <b class='Bib_author'>R. Fröberg, C. G. and Häggkvist, R.</b>,
<i class='Bib_title'>On numerical semigroups</i>,
<span class='Bib_journal'>Semigroup Forum</span>,
<em class='Bib_volume'>35</em> (<span class='Bib_number'>1</span>)
(<span class='Bib_year'>1987</span>),
<span class='Bib_pages'>63--83</span>.
</p>
<p><a id="biBRos96" name="biBRos96"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">Ros96a</span>] <b class='Bib_author'>Rosales, J. C.</b>,
<i class='Bib_title'>An algorithmic method to compute a minimal relation for any numerical
semigroup</i>,
<span class='Bib_journal'>Internat. J. Algebra Comput.</span>,
<em class='Bib_volume'>6</em>
(<span class='Bib_year'>1996</span>),
<span class='Bib_pages'>441-455</span>.
</p>
<p><a id="biBR96" name="biBR96"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">Ros96b</span>] <b class='Bib_author'>Rosales, J. C.</b>,
<i class='Bib_title'>On numerical semigroups</i>,
<span class='Bib_journal'>Semigroup Forum</span>,
<em class='Bib_volume'>52</em>
(<span class='Bib_year'>1996</span>),
<span class='Bib_pages'>307-318</span>.
</p>
<p><a id="biBRB03" name="biBRB03"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">RB03</span>] <b class='Bib_author'>Rosales, J. C. and Branco, M. B.</b>,
<i class='Bib_title'>Irreducible numerical semigroups</i>,
<span class='Bib_journal'>Pacific J. Math.</span>,
<em class='Bib_volume'>209</em> (<span class='Bib_number'>1</span>)
(<span class='Bib_year'>2003</span>),
<span class='Bib_pages'>131--143</span>.
</p>
<p><a id="biBRGS99" name="biBRGS99"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">RG99</span>] <b class='Bib_author'>Rosales, J. C. and Garc\'ia-S\'anchez, P. A.</b>,
<i class='Bib_title'>Finitely generated commutative monoids</i>,
<span class='Bib_publisher'>Nova Science Publishers</span>,
<span class='Bib_address'>New York</span>
(<span class='Bib_year'>1999</span>).
</p>
<p><a id="biBRGbook" name="biBRGbook"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">RSar</span>] <b class='Bib_author'>Rosales, J. C. and García Sánchez, P. A.</b>,
<i class='Bib_title'>Numerical Semigroups</i>,
<span class='Bib_publisher'>Springer</span>
(<span class='Bib_year'>To Appear</span>).
</p>
<p><a id="biBCGL" name="biBCGL"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">CL07</span>] <b class='Bib_author'>S. T. Chapman, P. A. G.-S. and Llena, D.</b>,
<i class='Bib_title'>The catenary and tame degree of numerical semigroups</i>,
<span class='Bib_journal'>Forum Math.</span>
(<span class='Bib_year'>2007</span>),
<span class='Bib_pages'>1--13</span>.
</p>
<p><a id="biBCHM06" name="biBCHM06"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">CM06</span>] <b class='Bib_author'>S. T. Chapman, M. T. H. and Moore, T. A.</b>,
<i class='Bib_title'>Full elasticity in atomic monoids and integral domains</i>,
<span class='Bib_journal'>Rocky Mountain J. Math.</span>,
<em class='Bib_volume'>36</em> (<span class='Bib_number'>5</span>)
(<span class='Bib_year'>2006</span>),
<span class='Bib_pages'>1437--1455</span>.
</p>
<p><a id="biBCGLPR" name="biBCGLPR"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">PR06</span>] <b class='Bib_author'>S. T. Chapman P. A. Garc\'ia-S\'anchez D. Llena V. Ponomarenko, and Rosales, J. C.</b>,
<i class='Bib_title'>The catenary and tame degree in finitely generated commutative
cancellative
monoids</i>,
<span class='Bib_journal'>Manuscripta Math.</span>,
<em class='Bib_volume'>120</em> (<span class='Bib_number'>3</span>)
(<span class='Bib_year'>2006</span>),
<span class='Bib_pages'>253--264</span>.
</p>
<p><a id="biBBDF97" name="biBBDF97"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">BF97</span>] <b class='Bib_author'>Valentina Barucci, D. E. D. and Fontana, M.</b>,
<i class='Bib_title'>Maximality properties in numerical semigroups and applications to
one-dimensional analytically irreducible local domains</i>,
<span class='Bib_publisher'>American Mathematical Society</span>,
<span class='Bib_series'>Memoirs of the American Mathematical Society</span> (<span class='Bib_number'>598</span>)
(<span class='Bib_year'>1997</span>).
</p>
<p><a id="biBVMic02" name="biBVMic02"></a></p>
<p class='Bib_entry'>
[<span class='Bib_key' style="color: #8e0000;">VMi02</span>] <b class='Bib_author'>VMicale, V.</b>,
<i class='Bib_title'>On monomial semigroups</i>,
<span class='Bib_journal'>Communications in Algebra</span>,
<em class='Bib_volume'>30</em>
(<span class='Bib_year'>2002</span>),
<span class='Bib_pages'>4687 - 4698</span>.
</p>
<p> </p>
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