Элементы дискретной математики. Часть I - 52 стр.

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(x
1
+ x
2
+ ...+ x
n
)
m
=
=(x
1
+ x
2
+ ...+ x
n
)(x
1
+ x
2
+ ...+ x
n
) ...(x
1
+ x
2
+ ...+ x
n
)

m
.
x
m
1
1
x
m
2
2
...x
m
n
n
m
1
x
1
,m
2
x
2
m
n
x
n
m
1
,m
2
,...,m
n
, m
1
+ m
2
+ ...+ m
n
= m.
P (m
1
,m
2
,...,m
n
)
(x
1
+ x
2
+ ...+ x
n
)
m
m
1
x
1
m
2
x
2
m
n
x
n
m
1
,m
2
,...,m
n
m
1
+ m
2
+ ...+ m
n
= m
P (m
1
,m
2
,...,m
n
).
n
m
=
m
1
+m
2
+...+m
n
=m
P (m
1
,m
2
,...,m
n
).
x
1
= x
2
= ...= x
n
=1.
P (m
1
,m
2
,...,m
n
)=
= P (m
1
− 1,m
2
,...,m
n
)+P (m
1
,m
2
− 1,...,m
n
)+...+ P (m
1
,m
2
,...,m
n
− 1).
(x
1
+ x
2
+ ...+ x
n
)
m−1
(x
1
+ x
2
+ ...+ x
n
)=(x
1
+ x
2
+ ...+ x
n
)
m
(x
1
+x
2
+...+x
n
)
m−1
(x
1
+x
2
+...+x
n
)
m
(x
1
+ x
2
+ ...+ x
n
)
x
m
1
1
x
m
2
2
...x
m
n
n
.
P (m
1
,m
2
,...,m
n
)=
k
i
+l
i
=m
i
P (k
1
,k
2
,...,k
n
)P (l
1
,l
2
,...,l
n
),
k
1
,k
2
,
k
n
; l
1
,l
2
,...,l
n
k
1
+ k
2
+ ... + k
n
= s, l
1
+ l
2
+ ... + l
n
= t
k
1
+ l
1
= m
1
,k
2
+ l
2
= m
2
, k
n
+ l
n
= m
n
.

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