Permutation Groups Generated by <i>γ</i>-Cycles
A <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-cycle is a cycle of the form <inline-formula><math xmlns="http://www.w3.org/...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/10/528 |
| _version_ | 1827651699168247808 |
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| author | Răzvan Diaconescu |
| author_facet | Răzvan Diaconescu |
| author_sort | Răzvan Diaconescu |
| collection | DOAJ |
| description | A <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-cycle is a cycle of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>i</mi><mo>+</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula> in the symmetric group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>n</mi></msub></semantics></math></inline-formula>. We study the subgroups of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>n</mi></msub></semantics></math></inline-formula> generated by several sets of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-cycles. Our mathematical development is strongly supported by computational experiments and proofs based on do-it-yourself programming with the logic-based language Maude. |
| first_indexed | 2024-03-09T20:43:16Z |
| format | Article |
| id | doaj.art-efef70045ce94f88a0657c45183aed68 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T20:43:16Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-efef70045ce94f88a0657c45183aed682023-11-23T22:53:50ZengMDPI AGAxioms2075-16802022-10-01111052810.3390/axioms11100528Permutation Groups Generated by <i>γ</i>-CyclesRăzvan Diaconescu0Simion Stoilow Institute of Mathematics of the Romanian Academy, 010702 Bucharest, RomaniaA <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-cycle is a cycle of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>i</mi><mo>+</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula> in the symmetric group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>n</mi></msub></semantics></math></inline-formula>. We study the subgroups of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>n</mi></msub></semantics></math></inline-formula> generated by several sets of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-cycles. Our mathematical development is strongly supported by computational experiments and proofs based on do-it-yourself programming with the logic-based language Maude.https://www.mdpi.com/2075-1680/11/10/528permutation groupsexperimental mathematicspreordered algebrarewriting |
| spellingShingle | Răzvan Diaconescu Permutation Groups Generated by <i>γ</i>-Cycles Axioms permutation groups experimental mathematics preordered algebra rewriting |
| title | Permutation Groups Generated by <i>γ</i>-Cycles |
| title_full | Permutation Groups Generated by <i>γ</i>-Cycles |
| title_fullStr | Permutation Groups Generated by <i>γ</i>-Cycles |
| title_full_unstemmed | Permutation Groups Generated by <i>γ</i>-Cycles |
| title_short | Permutation Groups Generated by <i>γ</i>-Cycles |
| title_sort | permutation groups generated by i γ i cycles |
| topic | permutation groups experimental mathematics preordered algebra rewriting |
| url | https://www.mdpi.com/2075-1680/11/10/528 |
| work_keys_str_mv | AT razvandiaconescu permutationgroupsgeneratedbyigicycles |