Advances and Applications in Discrete Mathematics
Volume 21, Issue 1, Pages 31 - 52
(May 2019) http://dx.doi.org/10.17654/ |
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EXPLICIT EXPRESSION FOR THE PRODUCT OF THE CLASS OF TWO TRANSPOSITIONS WITH THE CLASS OF CYCLES OF LENGTH k
Omar Tout and Rayane Abou-Nasser Al-Yafi
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Abstract: We give explicit formulas for the structure coefficients of the center of the symmetric group algebra involving the class of two transpositions. In particular, we show the explicit expression for the product of the class of two transpositions with the class of cycles of a given length k. In addition a formula for the structure coefficient for any partition λ of n is given. |
Keywords and phrases: The center of the symmetric group algebra, structure coefficients, product of conjugacy classes of the symmetric group, representation theory of the symmetric group.
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