1-Colored Archetypal Permutations and Strings of Degree n
New notions related to permutations are introduced here. We present the string of a 1-colored permutation as a closed planar curve, the fundamental 1-colored permutation as an equivalence class related to the equivalence in strings of the 1-colored permutations. We give formulas for the number of th...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2012-10-01
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| Series: | Memoirs of the Scientific Sections of the Romanian Academy |
| Subjects: | |
| Online Access: | http://mss.academiaromana-is.ro/mem_sc_st_2012/art%2001%20Tara.pdf |
| _version_ | 1819298623546982400 |
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| author | Gheorghe Eduard Tara |
| author_facet | Gheorghe Eduard Tara |
| author_sort | Gheorghe Eduard Tara |
| collection | DOAJ |
| description | New notions related to permutations are introduced here. We present the string of a 1-colored permutation as a closed planar curve, the fundamental 1-colored permutation as an equivalence class related to the equivalence in strings of the 1-colored permutations. We give formulas for the number of the 1-colored archetypal permutations of degree n. We establish an algorithm to identify the 1- colored archetypal permutations of degree n and we present the atlas of the 1-colored archetypal strings of degree n, n ≤ 7, based on this algorithm. |
| first_indexed | 2024-12-24T05:32:51Z |
| format | Article |
| id | doaj.art-b63205a7c80d4f44a1c5e659e1a694a5 |
| institution | Directory Open Access Journal |
| issn | 1224-1407 2343-7049 |
| language | English |
| last_indexed | 2024-12-24T05:32:51Z |
| publishDate | 2012-10-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Memoirs of the Scientific Sections of the Romanian Academy |
| spelling | doaj.art-b63205a7c80d4f44a1c5e659e1a694a52022-12-21T17:13:07ZengPublishing House of the Romanian AcademyMemoirs of the Scientific Sections of the Romanian Academy1224-14072343-70492012-10-01XXXV7311051-Colored Archetypal Permutations and Strings of Degree nGheorghe Eduard Tara0Department of Mathematics, „Babes-Bolyai” University, Cluj-Napoca, RomaniaNew notions related to permutations are introduced here. We present the string of a 1-colored permutation as a closed planar curve, the fundamental 1-colored permutation as an equivalence class related to the equivalence in strings of the 1-colored permutations. We give formulas for the number of the 1-colored archetypal permutations of degree n. We establish an algorithm to identify the 1- colored archetypal permutations of degree n and we present the atlas of the 1-colored archetypal strings of degree n, n ≤ 7, based on this algorithm.http://mss.academiaromana-is.ro/mem_sc_st_2012/art%2001%20Tara.pdfColored permutation groupMathematics Subject Classification 2010:20B30 |
| spellingShingle | Gheorghe Eduard Tara 1-Colored Archetypal Permutations and Strings of Degree n Memoirs of the Scientific Sections of the Romanian Academy Colored permutation group Mathematics Subject Classification 2010:20B30 |
| title | 1-Colored Archetypal Permutations and Strings of Degree n |
| title_full | 1-Colored Archetypal Permutations and Strings of Degree n |
| title_fullStr | 1-Colored Archetypal Permutations and Strings of Degree n |
| title_full_unstemmed | 1-Colored Archetypal Permutations and Strings of Degree n |
| title_short | 1-Colored Archetypal Permutations and Strings of Degree n |
| title_sort | 1 colored archetypal permutations and strings of degree n |
| topic | Colored permutation group Mathematics Subject Classification 2010:20B30 |
| url | http://mss.academiaromana-is.ro/mem_sc_st_2012/art%2001%20Tara.pdf |
| work_keys_str_mv | AT gheorgheeduardtara 1coloredarchetypalpermutationsandstringsofdegreen |