Equivalence of Carter diagrams
We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l>4 to an equivalent Carter diagram containing only 4-cycles. Transforming one Carter diagram Γ₁ to another Carter diagram Γ₂ we can get a...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155936 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Equivalence of Carter diagrams / R. Stekolshchik // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 1. — С. 138-179. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862743049524740096 |
|---|---|
| author | Stekolshchik, R. |
| author_facet | Stekolshchik, R. |
| citation_txt | Equivalence of Carter diagrams / R. Stekolshchik // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 1. — С. 138-179. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l>4 to an equivalent Carter diagram containing only 4-cycles. Transforming one Carter diagram Γ₁ to another Carter diagram Γ₂ we can get a certain intermediate diagram Γ′ which is not necessarily a Carter diagram. Such an intermediate diagram is called a connection diagram. The relation ρ is the equivalence relation on the set of Carter diagrams and connection diagrams. The properties of connection and Carter diagrams are studied in this paper. The paper contains an alternative proof of Carter's classification of admissible diagrams.
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| first_indexed | 2025-12-07T20:28:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155936 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:28:00Z |
| publishDate | 2017 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Stekolshchik, R. 2019-06-17T15:36:30Z 2019-06-17T15:36:30Z 2017 Equivalence of Carter diagrams / R. Stekolshchik // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 1. — С. 138-179. — Бібліогр.: 8 назв. — англ. 1726-3255 2010 MSC:20F55. https://nasplib.isofts.kiev.ua/handle/123456789/155936 We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l>4 to an equivalent Carter diagram containing only 4-cycles. Transforming one Carter diagram Γ₁ to another Carter diagram Γ₂ we can get a certain intermediate diagram Γ′ which is not necessarily a Carter diagram. Such an intermediate diagram is called a connection diagram. The relation ρ is the equivalence relation on the set of Carter diagrams and connection diagrams. The properties of connection and Carter diagrams are studied in this paper. The paper contains an alternative proof of Carter's classification of admissible diagrams. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Equivalence of Carter diagrams Article published earlier |
| spellingShingle | Equivalence of Carter diagrams Stekolshchik, R. |
| title | Equivalence of Carter diagrams |
| title_full | Equivalence of Carter diagrams |
| title_fullStr | Equivalence of Carter diagrams |
| title_full_unstemmed | Equivalence of Carter diagrams |
| title_short | Equivalence of Carter diagrams |
| title_sort | equivalence of carter diagrams |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155936 |
| work_keys_str_mv | AT stekolshchikr equivalenceofcarterdiagrams |