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## Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three

#### Omar TOUT [1]

We use the combinatorial way to give an explicit expression for the product of the class of cycles of length three with an arbitrary class of cycles. In addition, an explicit formula for the coefficient of an arbitrary class in the expansion of the product of an arbitrary class by the class of cycles of length three is given.

The center of the symmetric group algebra, Structure coefficients, Product of conjugacy classes of the symmetric group, Representation theory of the symmetric group
• [1] Z. Arad, M. Herzog (Eds.), Products of Conjugacy Classes in Groups, Lecture Notes in Math., vol. 1112, Springer-Verlag, Berlin, 1985.
• [2] E. A. Bertram, V. K. Wei, Decomposing a permutation into two large cycles: An enumeration, SIAM J. Algebraic Discrete Methods 1(4)(1980) 450–461.
• [3] G. Boccara, Nombre de representations d’une permutation comme produit de deux cycles de longueurs donnees, Discrete Math. 29(2) (1980) 105–134.
• [4] R. Cori, Un code pour les graphes planaires et ses applications, Astérisque 27 (1975) 169pp.
• [5] H. K. Farahat, G. Higman, The centres of symmetric group rings, Proc. Roy. Soc. London Ser. A 250(1261) (1959) 212–221.
• [6] A. Goupil, G. Schaeffer, Factoring n-cycles and counting maps of given genus, European J. Combin. 19(7) (1998) 819–834.
• [7] D. M. Jackson, T. I. Visentin, Character theory and rooted maps in an orientable surface of given genus: Face-colored maps, Trans. Amer. Math. Soc. 322(1) (1990) 365–376.
• [8] J. Katriel, J. Paldus, Explicit expression for the product of the class of transpositions with an arbitrary class of the symmetric group, R Gilmore (Ed.), Group Theoretical Methods in Physics, World Scientific, Singapore (1987) 503–506.
• [9] R. P. Stanley, Factorization of permutations into n-cycles, Discrete Math. 37(2-3) (1981) 255–262.
• [10] W. A. Stein et al., Sage Mathematics Software (Version 4.8), The Sage Development Team, http://www.sagemath.org.
• [11] O. Tout, Polynomialité des coefficients de structure des algèbres de doubles-classes. Ph.D thesis, Université de Bordeaux, 2014.
• [12] O. Tout, A general framework for the polynomiality property of the structure coefficients of double– class algebras, J. Algebr. Comb. 45(4) (2017) 1111–1152.
Primary Language en Engineering Articles Orcid: 0000-0003-0963-9639Author: Omar TOUT Publication Date : May 7, 2019
 Bibtex @research article { jacodesmath560404, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2019}, pages = {53 - 62}, doi = {10.13069/jacodesmath.560404}, title = {Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three}, key = {cite}, author = {Tout, Omar} } APA Tout, O . (2019). Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three . Journal of Algebra Combinatorics Discrete Structures and Applications , 6 (2) , 53-62 . DOI: 10.13069/jacodesmath.560404 MLA Tout, O . "Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three" . Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019 ): 53-62 Chicago Tout, O . "Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three". Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019 ): 53-62 RIS TY - JOUR T1 - Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three AU - Omar Tout Y1 - 2019 PY - 2019 N1 - doi: 10.13069/jacodesmath.560404 DO - 10.13069/jacodesmath.560404 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 53 EP - 62 VL - 6 IS - 2 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.560404 UR - https://doi.org/10.13069/jacodesmath.560404 Y2 - 2019 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three %A Omar Tout %T Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three %D 2019 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 6 %N 2 %R doi: 10.13069/jacodesmath.560404 %U 10.13069/jacodesmath.560404 ISNAD Tout, Omar . "Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three". Journal of Algebra Combinatorics Discrete Structures and Applications 6 / 2 (May 2019): 53-62 . https://doi.org/10.13069/jacodesmath.560404 AMA Tout O . Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(2): 53-62. Vancouver Tout O . Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(2): 53-62. IEEE O. Tout , "Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three", Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 6, no. 2, pp. 53-62, May. 2019, doi:10.13069/jacodesmath.560404

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