Geodesic
Polynomiality of irreducible characters of the symmetric groups
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Tome 378 (2010), pp. 32-39 
E. E. Goryachko. Polynomiality of irreducible characters of the symmetric groups. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Tome 378 (2010), pp. 32-39. http://geodesic.mathdoc.fr/item/ZNSL_2010_378_a2/
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     author = {E. E. Goryachko},
     title = {Polynomiality of irreducible characters of the symmetric groups},
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     pages = {32--39},
     year = {2010},
     volume = {378},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_378_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Consider Young diagrams differing only by the length of the first row (i.e., the form of diagrams below the first row is fixed). We prove that the values of the irreducible characters of the groups $\mathrm S_n$ corresponding to these diagrams are given by a polynomial of a special form with respect to natural parameters related to the cycle notation of permutations. Bibl. 3 titles.

[1] E. E. Goryachko, F. V. Petrov, “Nerazlozhimye kharaktery gruppy ratsionalnykh perekladyvanii otrezka”, Zap. nauchn. semin. POMI, 378, 2010, 17–31

[2] I. Makdonald, Simmetricheskie funktsii i mnogochleny Kholla, Mir, M., 1985 | MR

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