Investigation of insertion tableau evolution in the Robinson-Schensted-Knuth correspondence
Robinson-Schensted-Knuth (RSK) correspondence occurs in different contexts of algebra and combinatorics. Recently, this topic has been actively investigated by many researchers. At the same time, many investigations require conducting the computer experiments involving very large Young tableaux. The...
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| Format: | Article |
| Language: | English |
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Peoples’ Friendship University of Russia (RUDN University)
2019-12-01
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| Series: | Discrete and Continuous Models and Applied Computational Science |
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| Online Access: | http://journals.rudn.ru/miph/article/viewFile/22914/17808 |
| _version_ | 1811257489305370624 |
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| author | Vasilii S. Duzhin |
| author_facet | Vasilii S. Duzhin |
| author_sort | Vasilii S. Duzhin |
| collection | DOAJ |
| description | Robinson-Schensted-Knuth (RSK) correspondence occurs in different contexts of algebra and combinatorics. Recently, this topic has been actively investigated by many researchers. At the same time, many investigations require conducting the computer experiments involving very large Young tableaux. The article is devoted to such experiments. RSK algorithm establishes a bijection between sequences of elements of linearly ordered set and the pairs of Young tableaux of the same shape called insertion tableau and recording tableau . In this paper we study the dynamics of tableau and the dynamics of different concrete values in tableau during the iterations of RSK algorithm. Particularly, we examine the paths within tableaux called bumping routes along which the elements of an input sequence pass. The results of computer experiments with Young tableaux of sizes up to 108 were presented. These experiments were made using the software package for dealing with 2D and 3D Young diagrams and tableaux. |
| first_indexed | 2024-04-12T17:58:15Z |
| format | Article |
| id | doaj.art-2484ca7240034b7aa7e83f5116821080 |
| institution | Directory Open Access Journal |
| issn | 2658-4670 2658-7149 |
| language | English |
| last_indexed | 2024-04-12T17:58:15Z |
| publishDate | 2019-12-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | Discrete and Continuous Models and Applied Computational Science |
| spelling | doaj.art-2484ca7240034b7aa7e83f51168210802022-12-22T03:22:16ZengPeoples’ Friendship University of Russia (RUDN University)Discrete and Continuous Models and Applied Computational Science2658-46702658-71492019-12-0127431632410.22363/2658-4670-2019-27-4-316-32418477Investigation of insertion tableau evolution in the Robinson-Schensted-Knuth correspondenceVasilii S. Duzhin0Saint Petersburg Electrotechnical University “LETI”Robinson-Schensted-Knuth (RSK) correspondence occurs in different contexts of algebra and combinatorics. Recently, this topic has been actively investigated by many researchers. At the same time, many investigations require conducting the computer experiments involving very large Young tableaux. The article is devoted to such experiments. RSK algorithm establishes a bijection between sequences of elements of linearly ordered set and the pairs of Young tableaux of the same shape called insertion tableau and recording tableau . In this paper we study the dynamics of tableau and the dynamics of different concrete values in tableau during the iterations of RSK algorithm. Particularly, we examine the paths within tableaux called bumping routes along which the elements of an input sequence pass. The results of computer experiments with Young tableaux of sizes up to 108 were presented. These experiments were made using the software package for dealing with 2D and 3D Young diagrams and tableaux.http://journals.rudn.ru/miph/article/viewFile/22914/17808robinson-schensted-knuth correspondenceyoung tableauxyoung graphmarkov processcentral measureplancherel measureasymptotic representation theory |
| spellingShingle | Vasilii S. Duzhin Investigation of insertion tableau evolution in the Robinson-Schensted-Knuth correspondence Discrete and Continuous Models and Applied Computational Science robinson-schensted-knuth correspondence young tableaux young graph markov process central measure plancherel measure asymptotic representation theory |
| title | Investigation of insertion tableau evolution in the Robinson-Schensted-Knuth correspondence |
| title_full | Investigation of insertion tableau evolution in the Robinson-Schensted-Knuth correspondence |
| title_fullStr | Investigation of insertion tableau evolution in the Robinson-Schensted-Knuth correspondence |
| title_full_unstemmed | Investigation of insertion tableau evolution in the Robinson-Schensted-Knuth correspondence |
| title_short | Investigation of insertion tableau evolution in the Robinson-Schensted-Knuth correspondence |
| title_sort | investigation of insertion tableau evolution in the robinson schensted knuth correspondence |
| topic | robinson-schensted-knuth correspondence young tableaux young graph markov process central measure plancherel measure asymptotic representation theory |
| url | http://journals.rudn.ru/miph/article/viewFile/22914/17808 |
| work_keys_str_mv | AT vasiliisduzhin investigationofinsertiontableauevolutionintherobinsonschenstedknuthcorrespondence |