Dense numerical semigroups
A numerical semigroup S is dense if for all s ∈ S \ { 0 } we have s - 1 , s + 1 ∩ S ≠ ∅ . We give algorithms to compute the whole set of dense numerical semigroups with fixed genus, Frobenius number and multiplicity. Furthermore, we solve the Frobenius problem for dense numerical semigroups with emb...
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| Veröffentlicht in: | Semigroup forum 2021, Vol.103 (1), p.221-235 |
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| container_title | Semigroup forum |
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| creator | Rosales, J. C. Branco, M. B. Faria, M. C. |
| description | A numerical semigroup S is dense if for all
s
∈
S
\
{
0
}
we have
s
-
1
,
s
+
1
∩
S
≠
∅
. We give algorithms to compute the whole set of dense numerical semigroups with fixed genus, Frobenius number and multiplicity. Furthermore, we solve the Frobenius problem for dense numerical semigroups with embedding dimension three. |
| doi_str_mv | 10.1007/s00233-021-10190-1 |
| format | Article |
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s
∈
S
\
{
0
}
we have
s
-
1
,
s
+
1
∩
S
≠
∅
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s
∈
S
\
{
0
}
we have
s
-
1
,
s
+
1
∩
S
≠
∅
. We give algorithms to compute the whole set of dense numerical semigroups with fixed genus, Frobenius number and multiplicity. Furthermore, we solve the Frobenius problem for dense numerical semigroups with embedding dimension three.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Research Article</subject><subject>Semigroups</subject><issn>0037-1912</issn><issn>1432-2137</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKt_oKeC5-jMJJtsjlI_oeBFzyHszpYt3Q-T7sF_b3QFb56Ggfd5X3iEWCHcIIC9TQCklARCiYAOJJ6IBWpFklDZU7EAUFaiQzoXFyntIf9g1EKs7rlPvO6njmNbhcM6cdfu4jCN6VKcNeGQ-Or3LsX748Pb5lluX59eNndbWZGFo3R14Zx2eR5KVbKDsgEqDVtlQddA3FBh2HAowFYFqlAZqzEYxFojalBLcT33jnH4mDgd_X6YYp8nPRVaUy6zZU7RnKrikFLkxo-x7UL89Aj-24GfHfjswP848JghNUMph_sdx7_qf6gvZMxa7w</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Rosales, J. C.</creator><creator>Branco, M. B.</creator><creator>Faria, M. C.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2021</creationdate><title>Dense numerical semigroups</title><author>Rosales, J. C. ; Branco, M. B. ; Faria, M. C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-9d599492330838e908f0286e73704d02ef256e6ea507c513ac6741a611d411403</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Research Article</topic><topic>Semigroups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rosales, J. C.</creatorcontrib><creatorcontrib>Branco, M. B.</creatorcontrib><creatorcontrib>Faria, M. C.</creatorcontrib><collection>CrossRef</collection><jtitle>Semigroup forum</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rosales, J. C.</au><au>Branco, M. B.</au><au>Faria, M. C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dense numerical semigroups</atitle><jtitle>Semigroup forum</jtitle><stitle>Semigroup Forum</stitle><date>2021</date><risdate>2021</risdate><volume>103</volume><issue>1</issue><spage>221</spage><epage>235</epage><pages>221-235</pages><issn>0037-1912</issn><eissn>1432-2137</eissn><abstract>A numerical semigroup S is dense if for all
s
∈
S
\
{
0
}
we have
s
-
1
,
s
+
1
∩
S
≠
∅
. We give algorithms to compute the whole set of dense numerical semigroups with fixed genus, Frobenius number and multiplicity. Furthermore, we solve the Frobenius problem for dense numerical semigroups with embedding dimension three.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00233-021-10190-1</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0037-1912 |
| ispartof | Semigroup forum, 2021, Vol.103 (1), p.221-235 |
| issn | 0037-1912 1432-2137 |
| language | eng |
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| source | SpringerLink Journals |
| subjects | Algebra Algorithms Mathematics Mathematics and Statistics Research Article Semigroups |
| title | Dense numerical semigroups |
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