Geodesic
On the character tables of symmetric groups
Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 211-225.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, some zeros and non-zeros in the character tables of symmetric groups are displayed in the partition forms. In particular, more zeros of self conjugate partitions beside odd permutations are heavily investigated.
Keywords: characters, symmetric group, self conjugate partitions.
Mots-clés : partitions 
@article{ADM_2021_32_2_a3,
     author = {K. Kawsathon and K. Rodtes},
     title = {On the character tables of symmetric groups},
     journal = {Algebra and discrete mathematics},
     pages = {211--225},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a3/}
}
TY  - JOUR
AU  - K. Kawsathon
AU  - K. Rodtes
TI  - On the character tables of symmetric groups
JO  - Algebra and discrete mathematics
PY  - 2021
SP  - 211
EP  - 225
VL  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a3/
LA  - en
ID  - ADM_2021_32_2_a3
ER  - 
%0 Journal Article
%A K. Kawsathon
%A K. Rodtes
%T On the character tables of symmetric groups
%J Algebra and discrete mathematics
%D 2021
%P 211-225
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a3/
%G en
%F ADM_2021_32_2_a3
K. Kawsathon; K. Rodtes. On the character tables of symmetric groups. Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 211-225. http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a3/

[1] J. Brough, “Non-vanishing elements in finite groups”, J. Algebra, 460 (2016), 387–391 | DOI | MR | Zbl

[2] S. Dolfi, G. Navarro, E. Pacifici, L. Sanus, P. H. Tiep, “Non-vanishing elements of finite groups”, J. Algebra, 323:2 (2010), 540–545 | DOI | MR | Zbl

[3] S. Dolfi, E. Pacifici, L. Sanus, “Finite groups with real-valued irreducible characters of prime degree”, J. Algebra, 320 (2008), 2181–2195 | DOI | MR | Zbl

[4] I. M. Isaacs, Character Theory of Finite Groups, Dover, New York, 1976 | MR

[5] I. M. Isaacs, G. Navarro, “Groups whose real irreducible characters have degrees coprime to $p$”, J. Algebra, 356 (2012), 195–206 | DOI | MR | Zbl

[6] G. James, A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley Publishing Company, 1981 | MR | Zbl

[7] T. Y. Lam, K. H. Leung, “On Vanishing Sums of Roots of Unity”, J. Algebra, 224:1 (2000), 91–109 | DOI | MR | Zbl

[8] G. Malle, G. Navarro, J. B. Olsson, “Zeros of characters of finite groups”, J. Group Theory, 3 (2000), 353–368 | DOI | MR | Zbl

[9] L. Morotti, “Vanishing classes for $p$-singular characters of symmetric groups”, J. Algebra, 422 (2015), 334–340 | DOI | MR | Zbl

[10] L. Morotti, “$p$-Vanishing conjugacy classes of symmetric groups”, J. Algebra, 450 (2016), 349–383 | DOI | MR | Zbl

[11] M. Miyamoto, “Non-vanishing elements in finite groups”, J. Algebra, 364 (2012), 88–89 | DOI | MR | Zbl

[12] J. B. Olsson, Combinatorics and Representations of Finite Groups, Vorlesungen aus dem Fachbereich Mathematik der Univeritat GH Essen, 20, 1994 | MR

[13] G. Qian, Y. Wang, H. Wei, “Finite solvable groups with at most two nonlinear irreducible characters of each degree”, J. Algebra, 320 (2008), 3172–3186 | DOI | MR | Zbl

[14] B. Steinberg, “Representation Theory of Finite Groups: An Introductory Approach”, Universitext, Springer-Verlag, New York, 2012 | DOI | MR

[15] B. Sury, “Some Applications of Representation Theory to Classical Number Theory”, Unity of Mathematics' Lecture, AIS on Representation Theory (June 24, 2010)