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| NUMBERS OF CONJUGATE CLASSES OF SYMMETRIC AND ALTERNATING GROUPS |
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Citation： |
Wang Efang.NUMBERS OF CONJUGATE CLASSES OF SYMMETRIC AND ALTERNATING GROUPS[J].Chinese Annals of Mathematics B,1986,7(1):34~43 |
| Page view： 863
Net amount： 763 |
Authors： |
Wang Efang; |
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| Abstract： |
Let d(n) be the excess of the number of even conjugate classes of $\[{S_n}\]$ over that of odd conjugate classes of $\[{S_n}\]$, and q(n) the number of splitting classes of $\[{S_n}\]$. In this paper a recurrence formula for d(n) and one for q(n) are given. As a recurrence formula for the
number p(n) of conjugate classes of $\[{S_n}\]$ is known, one can make use of p(n), d(n) and q(n) to calculate the nunbers of even (odd) conjugate classes of $\[{S_n}\]$ and that of conjugate classes of $\[{A_n}\]$. By means of a graphical method the author proves the identity $\[d(n) = q(n)\]$ when $\[n \ge 2\]$, which seems to have been obtained first by Sylvester by use of generating functions. |
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