<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <title>GAP (NumericalSgps) - References</title> <meta http-equiv="content-type" content="text/html; charset=UTF-8" /> <meta name="generator" content="GAPDoc2HTML" /> <link rel="stylesheet" type="text/css" href="manual.css" /> </head> <body> <div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chap4.html">4</a> <a href="chap5.html">5</a> <a href="chap6.html">6</a> <a href="chap7.html">7</a> <a href="chap8.html">8</a> <a href="chap9.html">9</a> <a href="chapA.html">A</a> <a href="chapB.html">B</a> <a href="chapC.html">C</a> <a href="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div> <div class="chlinkprevnexttop"> <a href="chap0.html">Top of Book</a> <a href="chapC.html">Previous Chapter</a> <a href="chapInd.html">Next Chapter</a> </div> <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> <div class="chlinkprevnextbot"> <a href="chap0.html">Top of Book</a> <a href="chapC.html">Previous Chapter</a> <a href="chapInd.html">Next Chapter</a> </div> <div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chap4.html">4</a> <a href="chap5.html">5</a> <a href="chap6.html">6</a> <a href="chap7.html">7</a> <a href="chap8.html">8</a> <a href="chap9.html">9</a> <a href="chapA.html">A</a> <a href="chapB.html">B</a> <a href="chapC.html">C</a> <a href="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div> <hr /> <p class="foot">generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p> </body> </html>