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0 & ` :591,92,93,94,95
& ' & 24(:5)=D 4, & D 4:
@n1,…An

( & ' P

' & {A=( 1 , a2i, …, ani)| aj1i=aj2i=…=ajl i} @n1,…, An

$ A aj2i, aj3i, …, ajl i.

? 8 C @n + 5 , 6 8 4 + 5 ,

C 6 j1, …, jJ, + - , A + 5 j2, j3, …, jJ.

4 &.

D 491,92,91,93=

0, a, 0, b

1, b, 1, c

 

1, b, 1, d

 

0 & ` D 4 13(D 4)=G3, & G3:

G391,92,93 =

0, a, b

1, b, c

 

1, b, d

 

D A l=2, j1=1, j2=2, 9 12(@n) : 5 (@n). < 4 + (@n)

9 8 8 5- 9 .

>. > & ` n 9 ' & $, 8 & % &'-

' (a, …, a) n.

4 &. 1 & ` - & '. S 8 1,2,…n(@n)-

& ` 9, 1,2,…n(@n) n. _ , & % &'- & ` @n n

' (@n)—1=@n.

>. + P & K(@n) &

& ` Dn+1=K(@n) & A, A1, A2, ..., An , 8 & @n( 1 j, a2

j,

...,

an

j)

'

D n+1(a, a1 j, a2 j, ..., an j) & % &'- .

C + @n 9 M 4 :

C Dn+1=K(@n) 4, 9 : 9 4

A=(a1i, a2i, …, ani) @n1,…,An 8 + 5 ( , 1 , a2i, …, ani) Dn+1A,A1,…,An,

A 6 9 M.

4 &. 0 A3 9={0,1} P

A39= 1, 0, 0 0, 1, 0

0, 0, 1

' P ( 9) &

A49= 0, 1, 0, 0 0, 0, 1, 0

0, 0, 0, 1 1, 1, 0, 0 1, 0, 1, 0 1, 0, 0, 1

K, , +: C 6.

31

6.2.:F * F, % % . C ,

9 6 C & A.

-6 @n C 9 6 M1, M2, … , Mn-1, A, a Cm C

9 6 A, An, An+1, … , An+m-2.

>. + & A & & ` ' @n Cm &

& ` Dn+m-2=@nLCm & 91, 92, …, 9n+m-2, , 8 Dn+m-2(a1 , a2 ,…, ain+m-2j)

' & ' &, "& ' , & ' @n(a1 , a2 , …,

an-1 , a) Cm(a, an , an+1 , …, an+m-2 ).

 

 

 

 

 

4 &. An1,…,An=

1,

2,

2,

n

n+1

 

 

 

 

3,

 

 

 

…............................................................

 

 

 

 

k-2n+2k-2n+3…

k-n+1

 

:nAn, …, A1=

n,

 

n-1,

1

 

 

 

n+1,

 

n,

2

 

 

 

 

….............................................................

 

D 2n-2A1,…,An-1,An+1,…A1=1,

k-n+1, k-n,

k-2n+2

 

n,

2,

… n-1,

n-1 … 2,

1

2,

3,

n

… 3

2

 

…........................................................................

 

 

k-2n+2,

k-2n+3, …

k-n, k-n,

… k-2n+3, k-2n+2

 

4 &. d P ALE % ( & ` ' A E ( 9={a, b, c}

B={0, 1, 2}=C P

 

 

 

 

 

 

A9>= , 0

 

EBC=

0, 1

 

 

 

 

b, 1

 

0, 2

 

 

 

 

 

c, 2

 

1, 2

 

 

 

 

 

2, 2

 

 

 

 

 

 

 

&

 

(ALE)=

a, 1

 

 

 

a, 2

 

 

 

 

 

 

 

b, 2

 

 

 

 

 

 

 

c, 2

 

 

 

 

 

 

 

4 , .

1.@nLCm CmL@n

2.(@nLCm)LD k= @nL(CmLD k)

> 5

3. (@nLCm)-1=(Cm)-1L(@n)-1

-6 @ - 8 C 9 6 M, 1, C - 8 C

9 6 1, >. <4 8 6 C 5 @ C : 5 6 5 + $.

8 6 C 5 : C 4 5 n-

.

4 &. E ( " L1, L2, L3 – , M M’ - & ` & & & L1 L2 L2 L3. .& M<=MLM- & ` ' M M

& ` & L1 L3.

-6 @1m C 9 6 M1,…,Mm-1, B1; @2m 9 6 M1,…,Mm-1, B2;…;@n-1m 9 6 M1,…,Mm-1, Bn-1; Cn 9 6 (1,…,1n-1, Am.

>. N$ & ` ' @1m,@2m,…,@n-1m,Cn ' m-& `

Dm=Cn(@1m,@2m,…,@n-1m) ( 91,A2,…,9m , 8 Dm( 1 , a2 ,…,ami) & ' &,

"& ' b1j B1, b2j B2,…,bn-1j Bn-1, & ( @sm( 1 , a2 ,…,am-1i,bsj % &'-

s=1, 2,…,n-1, , Cn(b1j, b2j, bn-1j, am ).

32

4 &. @13 = 0, 1, 1

@23 = 0, 0, 0

@33 = 0, 0, 1

C 4= 0, 0, 0, 0

1, 0, 0

0, 1, 0

0, 1, 1

1, 0, 1, 1

1, 1, 1

1, 1, 1

 

1, 1, 0

1, 1, 0, 0

D 3=C4(@13,@23,@33)= 0, 1, 1

1, 1, 1

 

 

1, 1, 1, 1

 

 

 

 

1, 1, 0

 

 

 

 

1, 1, 1

6 C 5 : 4 -* 4.

+H . % ,

1.Y $ & n-( & ` ' &

$'?

2.S $' % n- & `?

3.S ' & n- & `?

4.

Y & $ & ` & ( & ` ' & ' ?

5.S & $ ' & ` (?

6.0 ( & ` ' & A?

7.S & A?

8.Y $ & ` ' $

$ & A?

% +

+

1.E -.9. 0 & . – N4%.: 4, 2001. - N.33-38.

2._ 0., 1 " d. _'$ . – A.: E, 1990. - N.43-46.

3.d ` >.A., U " d.W., a8 W. . 9 %, b, .

_.:E &, 1989. - N.35-44.

4.N " >.4. A " . – _.: .(, 1975. -

N.97-115.

5._` a.A. A b %. – A.: c-

&, 1987. - N.62, 63.

0 &

6.d % >.9. + b & " . – A.: >b `.`., 1986. - N.13-

20.

7.1 P d., 1 .. N & %. – A.: A, 1976. - N.42-

46.

0 ( '

8.A & & & ' ( % & «+ & » & & P P ( 6.0804, 6.0915 / +.A. A$ . – +&: +E43, 2001. – N.14-16.

33

? 7. " " " " J

" %

( " & n-(

& ` '. , 8 & & & & ",

& ` '. ) % &,

" n-( & ` ' P ', ', ',’', & ( % & `.

3 & & & :

7.1.3 & & ` '

7.2.N ' & ` '

7.1.% * + * K H

-6 @n - C 9 6 M1, M2, ..., Mn 4

@nA1, ..., An=

a1i1,

a2i1,

...

ani1

a1i2

a2i2,

...

ani2

 

 

.................................

 

 

 

a1ir

a2ir,

...

anir

 

 

>. 4$ & ` @n 9j ( % &'- j=1, 2, ..., n),

' rj(@n)={aji1, aji2, ajir} Aj ( j- @n1, An, % & ` @n 9j ' j-( (

& ` @n.

>. 4 ( ) S(j)a1 …,aj-1i,aj+1i,…,ani & ` @n (

a1 …,aj-1i,aj+1i,…,ani ' ( ajir Aj, & ( '

@n(a1 …,aj-1i,aji,aj+1i,…,ani), % S(j)a1 …,aj-1i,aj+1i,…,ani(@n)={ajir| @n(a1i,…,aj-1i,aj+1i,…,ani)}, & j=1, 2,…,n.

-6 Aj/@n={S(j) 1 …,aj-1i,aj+1i,…,ani(@n)}–9 . C @n 6

6

Mj-1× Aj+1× × An. * 9 Aj/@n : 5

( 1 …,aj-1i,aj+1i,…,ani)

M1× M2× ×

-9 + Aj

C + @n. < 5 : ( 1 …,aj-1i,aj+1i,…,ani) 9

4 6 +

5

`={( 1ir…,aj-1ir,aj+1ir,…,anir)/r=1,2,…,k}... .

S(j)X(@n)

C

` : 8': C @n 6 6, A 6 5 `:

S(j)X(@n)= r=1k (S(j) 1ir…,aj-1ir,aj+1ir,…,anir(@n)).

4 &. E ( " & ` A3 ( 9={a1, a2}, BB={b1, b2, b3} C={0,1}, 8

A3 B× C, &$

A3= a1, b1, 0 a1, b2, 0

a2, b1, 1 a2, b2, 1 a2, b2, 0,

& pr1(A3)=A, pr2(A3)={b1, b2}, pr3(A3)=C,

S(1)b2,0(A3)={a1,a2}, S(2)a1,0(A3)={b1,b2},

C/A3={S(3)a1,b1, S(3)a2,b1, S(3)a1,b2, S(3)a2,b2, S(3)a1,b3, S(3)a2,b3},

& X={(a1, b1),(a2, b1)} S(3)X(A3)=S(3)a1,b1 S(3)a2,b1=C.

>. > & ` Bn ( 91, 92,…,9n ' P '

& % " % & ` B2 ( (91× 92× × 9n) 9n, 8 &

& ( 1 …,a2i,…,an-1i) 91× 92× × 9n-1 S(n)a1 , a2i,…,an-1i(Bn)

' % '` & ani) 9n.

34

>.

S 8

&

% &'-

&

( 1 ,

a2i,…,an-1i)

91× 92× × An-1 S(n) 1 , a2i,…,an-1i(Bn)-", Bn

'

 

& ` & % " % & ` B2 ( (91×

92× × An-1)

9n.

 

 

 

 

 

 

>. S 8 S(n)X(Bn) =91× 92× × 9n-1 &$

9n, Bn $ & ` & % " % & ` B2

(

(91× 92× × 9n-1) 9n.

>. S 8 & % &'-( & ( & " ( 1 , a2i,…,an-1i),( 1j,

a2j,…,an-1j) 91× 92× × 9n-1 S(n) 1 , a2i,…,an-1i(Bn) S(n) 1j, a2j,…,an-1j(Bn)= ,

Bn & ` & % " % & ` B2

( (91× 92× × 9n-1) 9n.

1 C Bn : % 8 9 4 8 C B2

9 6 (M1× M2× × Mn-1) Mn, A Bn 5 , 5, ’: +: 8 9 4 8 C B2 9 6 (M1× M2× × Mn-1)

Mn.

4 &. E ( " $' 9 = {a, b}, B = {1, 2}, C = {I, II, III}. .

& ` R3A,B,C = {(a, 1, II), (b, 2, I), (a, 2, III), (b, 1, I ))} & % ' % & ` R(A,B),C = {((a, 1), II), ((b, 2), I), ((a, 2), III), ((b, 1), I)}, 8 ' ,

$ ’ , P ', ’ , , , %.

>. E ( " Bn P ' & ` ( 91,…,9n

& % " % & ` B2 ( (91× 92× × 9n-1) 9n. -

FBn(x1,…,xn-1) ' ' $ & ` Bn, 8 ( "

9 , & =1, 2,…, n-1, FBn( 1, a2,…, an-1)=S(n) 1, a2,…, an-1(Bn) & % &'- % ( 1, a2,…, an-1) 91× A2× × 9n-1.

4 &. E ( " & ` B3A,B,C = {(a, 2, II), (b, 1, I), (c, 1, III)} ( A = {a, b, c}, B = {1, 2}, C = {I, II, III} & % ' %

& ` B2(A,B),C = {((a, 2), II), ((b, 1), I), ((c, 1), III)} ( A× B = {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)} C = {I, II,

II}. .& & ` B3 P FB3(x1, x2), x1 A, x2 B, x3 C, FB3(a,2)=

S(3)a,2(B3)= II, FB3(b,1)= S(3)b,1(B3)= I, FB3(c,1)= S(3)c,1(B3)= III. 0 ` ( % A× B

P FB3(x1, x2) & .

D A C B1m, B2m,…, Bn-1m, Bn 5 ' FB1m,

FB2m,…,FBn-1m,FBn

,

 

 

Bn(B1m, B2m,…,Bn-1m) 9

: 5

C. < :+ Bn(B1m,

B2m,…,Bn-1m)

'

 

 

FBn(FB1m, FB2m,…,FBn-1m).

 

 

 

A. E ) . ) / 9 2

. ) / 9.

-6 B - 8 C 9 6 M, 1.

>. > & ` B ' & % 9 >, 8 - P ' " ' , % & % &'- 9 4 Sa(B) – "

' & sa(B)=b B.

T b=(a)B (8 b=B(a)) : 5 % 9 B

8 9 B, – % b.

>. N ' ( 9 (, 8 ( )B=b, ' %

b 9 & % B.

>. > & % B 9 > ' & % 9 >, 8 & $ $ ’ .

35

4 &. E ( " A = {a, b, c}, B = {1, 2}, & ` B & '

P BA,B = {(a, 2), (b, 1), (c, 2)}. .& B & % A B, % b 1, % B(a)=1, % 2 $ {a, c}, % B-1(2)={a, c}.

A. + B 2

(+ 2), 1 2.

<, : 8 9 M M : 4 5 C M,

A + 5 & % 9 %.

. + B 2- ( )

/) / , / B°B#1= , B -1°B = !,

, ! - + .

; /. : 1 = , 9 B - 2 +

+ / , / B°B#1=B -1°B= .

4 &. > & % B A = {a, b, c}

B = {1, 2, 3} P BA,B ={(a, 3), (b, 1), (c, 2)} &, B°B#1= ={a, b, c}, B -1°B = ! ={1, 2, 3}.

7.2. % C +H + * K H

>. n-& ` @An 9 ':

# P , 8 & % &'- '

@An( , ,…, ), % n @ n;

#P , 8 , & ' @An( , ,…, ), % n @ n= ;

#P (P ), 8 & & (, & (

' @An( , ,…, ), % n @ n n @ n .

4 &. E ( " A = {a, b}. . & ` @1A3 = {(a,a,a), (b,b,b), (a,b,b), (b,a,b)}, @2An = {(a,b,b), (b,b,b), (a,b,a), (b,a,b)}, @3An = {(a,b,a), (b,b,b), (a,b,b), (b,a,b)}

& & P , P , P .

 

 

>. 1 & ` @A 9 ':

 

 

#

P ,

8

&

% &'-

 

'

@A( , ), % @ ;

#P , 8 , & ' @A( , ),

% @ = ;

# P (P ), 8 & & (, & (

' @A( , ), % @ @ .

4 &. E ( " A = {a, b}. 1 & ` @1A = {(a,a), (b,b), (a,b)},

@2A = {(a,b), (b,a)}, @3A = {(a,b), (b,b), (b,a)} & & P , P ,

P .

>. n-& ` @An 9 ':

#, 8 & @An( 1 , 2 ,…, n ) P @An

'

 

% &'-

 

 

( 1 , 2 ,…, n );

#, 8 & ( 1 , 2 ,…, n ), &

& @An( 1 , 2 ,…, n ), P @An ' ( % & ( 1 ,

2 ,…, n );

# , 8 , , % & & ( ' ' , & & (

' .

36

4 &. E ( " A = {a, b}. . & ` @1A3 = ={(a,a,b), (b,b,b), (a,b,a), (b,a,a)}, @2An = {(a,b,b), (b,b,b), (a,b,a)}, @3An = {(a,b,a), (b,b,b), (a,b,b), (b,a,b), (b,b,a)}

& & , , .

>. 1 & ` @A 9 ':

#, 8 & @A( 1, 2) P @A '

( 2, 1);

#, 8 & ( 1, 2), &

& @A( 1, 2), P @A ' ( 2, 1);

#, 8 , , % & & ( ' ' , & & (

' .

4 &. E ( " A = {a, b, c}. 1 & ` @1A = ={(a,a), (b,a), (a,b)}, @2A = {(a,b), (b,b), (c,c)}, @3A = {(a,b), (b,b), (b,a), (c,a)} & & ,

, .

>. 1 & ` @A 9 ' , 8

& @A(a, b) @A(b, ) & ' @A( , ) & % &'-( a, b, c , ` & ` .

>. 1 & ` @A 9 ' ' , 8 & % &'-( a, b & @A(a, b) @A(b, ), ` & ` ' .

4 &. E ( " A = {a, b, c, d}. 1 & ` @1A = {(a,c), (b,a), (c,d), (b, c), (b, d), (a, d)}, @2A = {(a,b), (b,c), (c,d), (a,c)} & & .

4 &. E ( " A = {a, b, c, d}. . % & ` & '

& @1A = {(a,c), (b,a), (c,d), (b, c), (b, d), (a, d)}, @2A = {(a,b), (b,c), (c,d), (a,c)} & & ’ ' .

D A C @An 5 : 9 6 6 , 8

C (@An)-1 5 : + 9 5.

+H . % ,

1.Y $, , %& P- $ & n-(

& ` '?

2.S n- & ` P ', ’ ?

3.S n- & ` ' , $ ’ ?

4.S P ' ' $ n- & ` Bn?

5.3 & % 9 > & %

9 >?

6.Y % % & & `, ' %

% n- & `?

7.3 P , P P

% (n- ) & `?

8.Y , % (n- ) & `?

9.Y ' ' & % ( & ` '?

10.S $ "$ & % ( & ` '?

37

% +

+

1.E -.9. 0 & . – N4%.: 4, 2001. - N.35-38.

2._ 0., 1 " d. _'$ . – A.: E, 1990. - .43-46.

3.d ` >.A., U " d.W., a8 W. . 9 %, b, .

_.:E. &, 1989. - N.35-50.

4.N " >.4. A " . – _.: .(, 1975. -

N.97-115.

5._` a.A. A b %. – A.: c &, 1987. - N.62, 63.

0 &

6.d % >.9. + b & " . – A.: >b `. `., 1986. - N.13-

20.

7.1 P d., 1 .. N & %. – A.: A, 1976. - N.42-

46.

0 ( '

8.A & & & ' ( % & «+ & » & & P P ( 6.0804, 6.0915 / +.A. A$ . – +&: +E43, 2001. – N.15-17.

38

? 8. " " J

" %

' ( % ( & ` ', 8

$' ` `. ', " "

&, ', &, " ' ( & ` '. ) & , P &

' ( & ` '.

3 & & :

8.1.W '

8.2.4 &

8.3. . '

8.4._&

8.1. + H

>. 1 & ` @9 9, 8 & '

P , , ' & `

(N).

, A A @M - C 9 M, 8

C @M-1 9 : C 9.

1 C 9 M ' 8 : 9

9, A : 9 5 9 4 9 M

5 8.

-6 @M - C 9 M, A 9. 0 4 -9 M/@M={S (@M)| }.

>. 4 Sa(@A) ' & `$

@9.

A. G- /@ 9 3 / @ 2 + 3

/ Sa(@A)=A.

? A @M – , Sa(@ ) 9 4 4, ASa(@ ) Sb(@ ), : 5 @M b@ c, @ @Mb,

@ b Sa(@A)3Sb(@A), b@Aa Sb(@ )3Sa(@A), 8 Sa(@ )=Sb(@A), 9 + 5.

9 8 R(A)={A1, A2,..., Ak} 9 M : C

C 9 M, 9 4 8 4 + 5 8, 8 C b 5 , ,b , =1, 2,..., k.

. 5 9 3 / 2 2

+ R(A) 0 , , +-* + )

2 9 / .

<' C 5 8 9 9

5 4 , A 9, A 9

5 , 9. ( 5 9

: 9 5 (5 ), 8

6 9 : 5 - 9 6 4

.

-6 @ - C 9 M, A/@={Sa(@)/a } - -

9 9 M C + .

>. > & % 9 P- 9/@, 8

" Sa(@), ' , '

& & % 9 P- 9/@.

39

-6 B - 8 9 9 M 9 1. 1 8 9 + B :

C C 9 M. -6 1, 21C 2 5 , ( 1)B=( 2)B. . 9 b ! 4

4 8 8 9 B 6 5 :

8 9 P 9 1 -9 M/C, B°P 8 4 : 5

8 9 9 M -9 M/C.

1 , A 9 5 M 8 R={A1,..., An} 9 M,' C , A 9 6

: , 8 9 9 4 & ( ).

>. 4 & 9, 8 ' & ' &

9 & % ={A1, A2, ... , Ai,..., An} 9,

' $ & & & & ` .

4 &. ) E ( " 9 = { 1, 2, 3} B = {b1, b2, b3,b4 b5, b6, b7}. 1={ 1,

2, 3}, @9,1={< 1, a1>, <a1, a2>, <a1, a3>, <a2, a1>, <a2, a2>, <a2, a3>,<a3, a1>,<a3, a2>, <a3, a3>}; P2={{a1}, {a2}, {a3}}, @A,2={<a1, a1>, <a2, a2>, <a3, a3>}; PB={{b1, b2, b3}, {b4}, {b5, b6,

b7}}; @B={(b1, b1), (b1, b2), (b2, b1), (b2, b2), (b1, b3), (b3, b1), (b3, b3), (b2, b3), (b3, b2), (b4, b4), (b5, b5), (b5, b6), (b6, b5), (b6, b6), (b5, b7), (b7, b5), (b7, b7),

(b6, b7), (b7, b6)}

 

 

 

%)

 

. % 8.1.

 

 

 

 

 

 

@B

 

b1

b2

B3

b4

b5

B6

b7

b1

 

1

1

1

 

 

 

 

b2

 

1

1

1

 

 

 

 

b3

 

1

1

1

1

 

 

 

b4

 

 

 

 

1

1

1

b5

 

 

 

 

 

b6

 

 

 

 

 

1

1

1

b7

 

 

 

 

 

1

1

1

)

0. 8.1. 1 C @B

40

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