Eintrag weiter verarbeiten
Onn-Sums in an Abelian Group
Gespeichert in:
| Zeitschriftentitel: | Combinatorics, Probability and Computing |
|---|---|
| Personen und Körperschaften: | , , |
| In: | Combinatorics, Probability and Computing, 25, 2016, 3, S. 419-435 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Cambridge University Press (CUP)
|
| Schlagwörter: |
| author_facet |
GAO, WEIDONG GRYNKIEWICZ, DAVID J. XIA, XINGWU GAO, WEIDONG GRYNKIEWICZ, DAVID J. XIA, XINGWU |
|---|---|
| author |
GAO, WEIDONG GRYNKIEWICZ, DAVID J. XIA, XINGWU |
| spellingShingle |
GAO, WEIDONG GRYNKIEWICZ, DAVID J. XIA, XINGWU Combinatorics, Probability and Computing Onn-Sums in an Abelian Group Applied Mathematics Computational Theory and Mathematics Statistics and Probability Theoretical Computer Science |
| author_sort |
gao, weidong |
| spelling |
GAO, WEIDONG GRYNKIEWICZ, DAVID J. XIA, XINGWU 0963-5483 1469-2163 Cambridge University Press (CUP) Applied Mathematics Computational Theory and Mathematics Statistics and Probability Theoretical Computer Science http://dx.doi.org/10.1017/s0963548315000255 <jats:p>Let<jats:italic>G</jats:italic>be an additive abelian group, let<jats:italic>n</jats:italic>⩾ 1 be an integer, let<jats:italic>S</jats:italic>be a sequence over<jats:italic>G</jats:italic>of length |<jats:italic>S</jats:italic>| ⩾<jats:italic>n</jats:italic>+ 1, and let<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0963548315000255_inline1" /><jats:tex-math>${\mathsf h}$</jats:tex-math></jats:alternatives></jats:inline-formula>(<jats:italic>S</jats:italic>) denote the maximum multiplicity of a term in<jats:italic>S</jats:italic>. Let Σ<jats:italic><jats:sub>n</jats:sub></jats:italic>(<jats:italic>S</jats:italic>) denote the set consisting of all elements in<jats:italic>G</jats:italic>which can be expressed as the sum of terms from a subsequence of<jats:italic>S</jats:italic>having length<jats:italic>n</jats:italic>. In this paper, we prove that either<jats:italic>ng</jats:italic>∈ Σ<jats:sub><jats:italic>n</jats:italic></jats:sub>(<jats:italic>S</jats:italic>) for every term<jats:italic>g</jats:italic>in<jats:italic>S</jats:italic>whose multiplicity is at least<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0963548315000255_inline1" /><jats:tex-math>${\mathsf h}$</jats:tex-math></jats:alternatives></jats:inline-formula>(<jats:italic>S</jats:italic>) − 1 or |Σ<jats:italic><jats:sub>n</jats:sub></jats:italic>(<jats:italic>S</jats:italic>)| ⩾ min{<jats:italic>n</jats:italic>+ 1, |<jats:italic>S</jats:italic>| −<jats:italic>n</jats:italic>+ | supp (<jats:italic>S</jats:italic>)| − 1}, where |supp(<jats:italic>S</jats:italic>)| denotes the number of distinct terms that occur in<jats:italic>S</jats:italic>. When<jats:italic>G</jats:italic>is finite cyclic and<jats:italic>n</jats:italic>= |<jats:italic>G</jats:italic>|, this confirms a conjecture of Y. O. Hamidoune from 2003.</jats:p> On<i>n</i>-Sums in an Abelian Group Combinatorics, Probability and Computing |
| doi_str_mv |
10.1017/s0963548315000255 |
| facet_avail |
Online |
| finc_class_facet |
Mathematik Informatik |
| format |
ElectronicArticle |
| fullrecord |
blob:ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTAxNy9zMDk2MzU0ODMxNTAwMDI1NQ |
| id |
ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTAxNy9zMDk2MzU0ODMxNTAwMDI1NQ |
| institution |
DE-D275 DE-Bn3 DE-Brt1 DE-D161 DE-Gla1 DE-Zi4 DE-15 DE-Pl11 DE-Rs1 DE-105 DE-14 DE-Ch1 DE-L229 |
| imprint |
Cambridge University Press (CUP), 2016 |
| imprint_str_mv |
Cambridge University Press (CUP), 2016 |
| issn |
0963-5483 1469-2163 |
| issn_str_mv |
0963-5483 1469-2163 |
| language |
English |
| mega_collection |
Cambridge University Press (CUP) (CrossRef) |
| match_str |
gao2016onnsumsinanabeliangroup |
| publishDateSort |
2016 |
| publisher |
Cambridge University Press (CUP) |
| recordtype |
ai |
| record_format |
ai |
| series |
Combinatorics, Probability and Computing |
| source_id |
49 |
| title |
Onn-Sums in an Abelian Group |
| title_unstemmed |
Onn-Sums in an Abelian Group |
| title_full |
Onn-Sums in an Abelian Group |
| title_fullStr |
Onn-Sums in an Abelian Group |
| title_full_unstemmed |
Onn-Sums in an Abelian Group |
| title_short |
Onn-Sums in an Abelian Group |
| title_sort |
on<i>n</i>-sums in an abelian group |
| topic |
Applied Mathematics Computational Theory and Mathematics Statistics and Probability Theoretical Computer Science |
| url |
http://dx.doi.org/10.1017/s0963548315000255 |
| publishDate |
2016 |
| physical |
419-435 |
| description |
<jats:p>Let<jats:italic>G</jats:italic>be an additive abelian group, let<jats:italic>n</jats:italic>⩾ 1 be an integer, let<jats:italic>S</jats:italic>be a sequence over<jats:italic>G</jats:italic>of length |<jats:italic>S</jats:italic>| ⩾<jats:italic>n</jats:italic>+ 1, and let<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0963548315000255_inline1" /><jats:tex-math>${\mathsf h}$</jats:tex-math></jats:alternatives></jats:inline-formula>(<jats:italic>S</jats:italic>) denote the maximum multiplicity of a term in<jats:italic>S</jats:italic>. Let Σ<jats:italic><jats:sub>n</jats:sub></jats:italic>(<jats:italic>S</jats:italic>) denote the set consisting of all elements in<jats:italic>G</jats:italic>which can be expressed as the sum of terms from a subsequence of<jats:italic>S</jats:italic>having length<jats:italic>n</jats:italic>. In this paper, we prove that either<jats:italic>ng</jats:italic>∈ Σ<jats:sub><jats:italic>n</jats:italic></jats:sub>(<jats:italic>S</jats:italic>) for every term<jats:italic>g</jats:italic>in<jats:italic>S</jats:italic>whose multiplicity is at least<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0963548315000255_inline1" /><jats:tex-math>${\mathsf h}$</jats:tex-math></jats:alternatives></jats:inline-formula>(<jats:italic>S</jats:italic>) − 1 or |Σ<jats:italic><jats:sub>n</jats:sub></jats:italic>(<jats:italic>S</jats:italic>)| ⩾ min{<jats:italic>n</jats:italic>+ 1, |<jats:italic>S</jats:italic>| −<jats:italic>n</jats:italic>+ | supp (<jats:italic>S</jats:italic>)| − 1}, where |supp(<jats:italic>S</jats:italic>)| denotes the number of distinct terms that occur in<jats:italic>S</jats:italic>. When<jats:italic>G</jats:italic>is finite cyclic and<jats:italic>n</jats:italic>= |<jats:italic>G</jats:italic>|, this confirms a conjecture of Y. O. Hamidoune from 2003.</jats:p> |
| container_issue |
3 |
| container_start_page |
419 |
| container_title |
Combinatorics, Probability and Computing |
| container_volume |
25 |
| format_de105 |
Article, E-Article |
| format_de14 |
Article, E-Article |
| format_de15 |
Article, E-Article |
| format_de520 |
Article, E-Article |
| format_de540 |
Article, E-Article |
| format_dech1 |
Article, E-Article |
| format_ded117 |
Article, E-Article |
| format_degla1 |
E-Article |
| format_del152 |
Buch |
| format_del189 |
Article, E-Article |
| format_dezi4 |
Article |
| format_dezwi2 |
Article, E-Article |
| format_finc |
Article, E-Article |
| format_nrw |
Article, E-Article |
| _version_ |
1792344944269066249 |
| geogr_code |
not assigned |
| last_indexed |
2024-03-01T17:15:15.88Z |
| geogr_code_person |
not assigned |
| openURL |
url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fvufind.svn.sourceforge.net%3Agenerator&rft.title=Onn-Sums+in+an+Abelian+Group&rft.date=2016-05-01&genre=article&issn=1469-2163&volume=25&issue=3&spage=419&epage=435&pages=419-435&jtitle=Combinatorics%2C+Probability+and+Computing&atitle=On%3Ci%3En%3C%2Fi%3E-Sums+in+an+Abelian+Group&aulast=XIA&aufirst=XINGWU&rft_id=info%3Adoi%2F10.1017%2Fs0963548315000255&rft.language%5B0%5D=eng |
| SOLR | |
| _version_ | 1792344944269066249 |
| author | GAO, WEIDONG, GRYNKIEWICZ, DAVID J., XIA, XINGWU |
| author_facet | GAO, WEIDONG, GRYNKIEWICZ, DAVID J., XIA, XINGWU, GAO, WEIDONG, GRYNKIEWICZ, DAVID J., XIA, XINGWU |
| author_sort | gao, weidong |
| container_issue | 3 |
| container_start_page | 419 |
| container_title | Combinatorics, Probability and Computing |
| container_volume | 25 |
| description | <jats:p>Let<jats:italic>G</jats:italic>be an additive abelian group, let<jats:italic>n</jats:italic>⩾ 1 be an integer, let<jats:italic>S</jats:italic>be a sequence over<jats:italic>G</jats:italic>of length |<jats:italic>S</jats:italic>| ⩾<jats:italic>n</jats:italic>+ 1, and let<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0963548315000255_inline1" /><jats:tex-math>${\mathsf h}$</jats:tex-math></jats:alternatives></jats:inline-formula>(<jats:italic>S</jats:italic>) denote the maximum multiplicity of a term in<jats:italic>S</jats:italic>. Let Σ<jats:italic><jats:sub>n</jats:sub></jats:italic>(<jats:italic>S</jats:italic>) denote the set consisting of all elements in<jats:italic>G</jats:italic>which can be expressed as the sum of terms from a subsequence of<jats:italic>S</jats:italic>having length<jats:italic>n</jats:italic>. In this paper, we prove that either<jats:italic>ng</jats:italic>∈ Σ<jats:sub><jats:italic>n</jats:italic></jats:sub>(<jats:italic>S</jats:italic>) for every term<jats:italic>g</jats:italic>in<jats:italic>S</jats:italic>whose multiplicity is at least<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0963548315000255_inline1" /><jats:tex-math>${\mathsf h}$</jats:tex-math></jats:alternatives></jats:inline-formula>(<jats:italic>S</jats:italic>) − 1 or |Σ<jats:italic><jats:sub>n</jats:sub></jats:italic>(<jats:italic>S</jats:italic>)| ⩾ min{<jats:italic>n</jats:italic>+ 1, |<jats:italic>S</jats:italic>| −<jats:italic>n</jats:italic>+ | supp (<jats:italic>S</jats:italic>)| − 1}, where |supp(<jats:italic>S</jats:italic>)| denotes the number of distinct terms that occur in<jats:italic>S</jats:italic>. When<jats:italic>G</jats:italic>is finite cyclic and<jats:italic>n</jats:italic>= |<jats:italic>G</jats:italic>|, this confirms a conjecture of Y. O. Hamidoune from 2003.</jats:p> |
| doi_str_mv | 10.1017/s0963548315000255 |
| facet_avail | Online |
| finc_class_facet | Mathematik, Informatik |
| format | ElectronicArticle |
| format_de105 | Article, E-Article |
| format_de14 | Article, E-Article |
| format_de15 | Article, E-Article |
| format_de520 | Article, E-Article |
| format_de540 | Article, E-Article |
| format_dech1 | Article, E-Article |
| format_ded117 | Article, E-Article |
| format_degla1 | E-Article |
| format_del152 | Buch |
| format_del189 | Article, E-Article |
| format_dezi4 | Article |
| format_dezwi2 | Article, E-Article |
| format_finc | Article, E-Article |
| format_nrw | Article, E-Article |
| geogr_code | not assigned |
| geogr_code_person | not assigned |
| id | ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTAxNy9zMDk2MzU0ODMxNTAwMDI1NQ |
| imprint | Cambridge University Press (CUP), 2016 |
| imprint_str_mv | Cambridge University Press (CUP), 2016 |
| institution | DE-D275, DE-Bn3, DE-Brt1, DE-D161, DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229 |
| issn | 0963-5483, 1469-2163 |
| issn_str_mv | 0963-5483, 1469-2163 |
| language | English |
| last_indexed | 2024-03-01T17:15:15.88Z |
| match_str | gao2016onnsumsinanabeliangroup |
| mega_collection | Cambridge University Press (CUP) (CrossRef) |
| physical | 419-435 |
| publishDate | 2016 |
| publishDateSort | 2016 |
| publisher | Cambridge University Press (CUP) |
| record_format | ai |
| recordtype | ai |
| series | Combinatorics, Probability and Computing |
| source_id | 49 |
| spelling | GAO, WEIDONG GRYNKIEWICZ, DAVID J. XIA, XINGWU 0963-5483 1469-2163 Cambridge University Press (CUP) Applied Mathematics Computational Theory and Mathematics Statistics and Probability Theoretical Computer Science http://dx.doi.org/10.1017/s0963548315000255 <jats:p>Let<jats:italic>G</jats:italic>be an additive abelian group, let<jats:italic>n</jats:italic>⩾ 1 be an integer, let<jats:italic>S</jats:italic>be a sequence over<jats:italic>G</jats:italic>of length |<jats:italic>S</jats:italic>| ⩾<jats:italic>n</jats:italic>+ 1, and let<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0963548315000255_inline1" /><jats:tex-math>${\mathsf h}$</jats:tex-math></jats:alternatives></jats:inline-formula>(<jats:italic>S</jats:italic>) denote the maximum multiplicity of a term in<jats:italic>S</jats:italic>. Let Σ<jats:italic><jats:sub>n</jats:sub></jats:italic>(<jats:italic>S</jats:italic>) denote the set consisting of all elements in<jats:italic>G</jats:italic>which can be expressed as the sum of terms from a subsequence of<jats:italic>S</jats:italic>having length<jats:italic>n</jats:italic>. In this paper, we prove that either<jats:italic>ng</jats:italic>∈ Σ<jats:sub><jats:italic>n</jats:italic></jats:sub>(<jats:italic>S</jats:italic>) for every term<jats:italic>g</jats:italic>in<jats:italic>S</jats:italic>whose multiplicity is at least<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0963548315000255_inline1" /><jats:tex-math>${\mathsf h}$</jats:tex-math></jats:alternatives></jats:inline-formula>(<jats:italic>S</jats:italic>) − 1 or |Σ<jats:italic><jats:sub>n</jats:sub></jats:italic>(<jats:italic>S</jats:italic>)| ⩾ min{<jats:italic>n</jats:italic>+ 1, |<jats:italic>S</jats:italic>| −<jats:italic>n</jats:italic>+ | supp (<jats:italic>S</jats:italic>)| − 1}, where |supp(<jats:italic>S</jats:italic>)| denotes the number of distinct terms that occur in<jats:italic>S</jats:italic>. When<jats:italic>G</jats:italic>is finite cyclic and<jats:italic>n</jats:italic>= |<jats:italic>G</jats:italic>|, this confirms a conjecture of Y. O. Hamidoune from 2003.</jats:p> On<i>n</i>-Sums in an Abelian Group Combinatorics, Probability and Computing |
| spellingShingle | GAO, WEIDONG, GRYNKIEWICZ, DAVID J., XIA, XINGWU, Combinatorics, Probability and Computing, Onn-Sums in an Abelian Group, Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability, Theoretical Computer Science |
| title | Onn-Sums in an Abelian Group |
| title_full | Onn-Sums in an Abelian Group |
| title_fullStr | Onn-Sums in an Abelian Group |
| title_full_unstemmed | Onn-Sums in an Abelian Group |
| title_short | Onn-Sums in an Abelian Group |
| title_sort | on<i>n</i>-sums in an abelian group |
| title_unstemmed | Onn-Sums in an Abelian Group |
| topic | Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability, Theoretical Computer Science |
| url | http://dx.doi.org/10.1017/s0963548315000255 |