Geodesic
The simplest Young diagrams and groups generated by their tableaux
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 151-161 Cet article a éte moissonné depuis la source Math-Net.Ru

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To study the combinatorics of Young diagrams, Anatoly Moiseevich Vershik proposed to consider groups generated by natural involutions of two-row Young tables. The definitions and the first results were described by A. M. Vershik and N. V. Tsilevich. In this paper the class of the studied diagrams is expanded and new methods for their characterization are given. 
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P. A. Pozdeev. The simplest Young diagrams and groups generated by their tableaux. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 151-161. http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a8/

[1] A. M. Vershik, N .V. Tsilevich, “Gruppy, porozhdennye involyutsiyami rombovidnykh grafov, i deformatsii ortogonalnoi formy Yunga”, Zap. nauchn. semin. POMI, 481, 2019

[2] Dzh. Khamfris, Vvedenie v teoriyu algebr Li i ikh predstavlenii, §12 p. 1, MTsNMO, 2003

[3] U. Fulton, Tablitsy Yunga i ikh prilozheniya k teorii predstavlenii i geometrii, MTsNMO, 2006

[4] R. Stenli, Perechislitelnaya kombinatorika, Mir, 1990