xyx+y(4)yx+yx.x+yxy
解
xyx+yyx+yxx+yxy
=x(x+y)y+yx(x+y)+(x+y)yx y3 (x+y)3 x3=3xy(x+y) y3 3x2y x3 y3 x3= 2(x3+y3).
2.按自然数从小到大为标准次序,求下列各排列的逆序数:
(1)1234;解逆序数为0(2)4132;解逆序数为4:(3)3421;解逆序数为5:(4)2413;解逆序数为3:
21,41,43.
(5)13 (2n 1)24 (2n);
n(n 1)
解逆序数为:
2
32(1个)52,54(2个)72,74,76(3个)
32,31,42,41,21.41,43,42,32.