ᒺ , , , .
ᒺ , , , , ᒺ , , .
ᒺ , ᒺ .
ᒺ (i, j = 1, 2,, n; ≠ j), (pij) ᒺ , i j.
, ᒺ , () , .
, , , , .
.
, d, d + k (k = 0, 1,...), , d, d - k (k = 0, 1,...).
, k , d, d + 1,..., d + k d, d - 1,..., d - k.
ᒺ , , , , , .
, , d , d + k (k = 0, 1,...) .
ϳ, ᒺ , , , .
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.
, ᒺ , 䒺 0, 1,..., - 1.
, d + k (k = 0, 1,...) d - k (k = 0, 1,...) 䒺 0, 1,..., - 1, , , d + k d - k , .
:
, ᒺ , , . 3
3
= 7 d + k d - k 7, ,
d = 1 (), k = 3, (d + k) mod 7 = 1 + 3 = 4 ();
d = 5 (), k = 3, (d + k) mod 7 = 5 + 3 - 7 = 1 ().
d = 5 (), k = 3, (d - k) mod 7 = 5 - 3 = 2 ();
d = 2 (), k = 3, (d - k) mod 7 = 2 - 3 + 7 = 6 ().
ᒺ .
. 3.
3
12 (1, 2,..., 12), 璺 5 :
1/2: 2 5 8 11 8 5 2;
3/4: 1 2 3 2 1;
5/6: 4 5 6 5 4;
7/8: 7 8 9 8 7;
9/10: 10 11 12 11 10.
, - - . 3 , , 24 , , , .
, ᒺ , , = 7, (pij) . 4, - ᒺ .
̳ , . |
4 ᒺ
. 4 , d .
4 , d
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- | d - 1 | d - 2 | d - 3 | d - 2 | d - 3 | d - 4 | d - 3 | d - 4 | d - 5 | d - 4 | d - 5 | |
d - 1 | - | d - 1 | d - 2 | d - 1 | d - 2 | d - 3 | d - 2 | d - 3 | d - 4 | d - 3 | d - 4 | |
d - 2 | d - 1 | - | d - 3 | d - 2 | d - 3 | d - 4 | d - 3 | d - 4 | d - 5 | d - 4 | d - 5 | |
d - 3 | d - 2 | d - 3 | - | d - 1 | d - 2 | d - 3 | d - 2 | d - 3 | d - 4 | d - 3 | d - 4 | |
d - 2 | d - 1 | d - 2 | d - 1 | - | d - 1 | d - 2 | d - 1 | d - 2 | d - 3 | d - 2 | d - 3 | |
d - 3 | d - 2 | d - 3 | d - 2 | d - 1 | - | d - 3 | d - 2 | d - 3 | d - 4 | d - 3 | d - 4 | |
d - 4 | d - 3 | d - 4 | d - 3 | d - 2 | d - 3 | - | d - 1 | d - 2 | d - 3 | d - 2 | d - 3 | |
d - 3 | d - 2 | d - 3 | d - 2 | d - 1 | d - 2 | d - 1 | - | d - 1 | d - 2 | d - 1 | d - 2 | |
d - 4 | d - 3 | d - 4 | d - 3 | d - 2 | d - 3 | d - 2 | d - 1 | - | d - 3 | d - 2 | d - 3 | |
d - 5 | d - 4 | d - 5 | d - 4 | d - 3 | d - 4 | d - 3 | d - 2 | d - 3 | - | d - 1 | d - 2 | |
d - 4 | d - 3 | d - 4 | d - 3 | d - 2 | d - 3 | d - 2 | d - 1 | d - 2 | d - 1 | - | d - 1 | |
d - 5 | d - 4 | d - 5 | d - 4 | d - 3 | d - 4 | d - 3 | d - 2 | d - 3 | d - 2 | d - 1 | - |
. 4 , d, , 8, 5, 7, 9, 11 d 1; 2, 4, 6, 10, 12 d 2; 1, 3 d - 3.
. 5 ᒺ (/) .
5 ᒺ
11/32 | 22/26 | 33/19 | 44/17 | 33/21 | 22/28 | 11/33 | 176/176 | |
11/26 | 22/18 | 33/16 | 44/20 | 33/29 | 22/34 | 11/33 | 176/176 | |
11/32 | 22/26 | 33/19 | 44/17 | 33/21 | 22/28 | 11/33 | 176/176 | |
11/30 | 22/20 | 33/14 | 44/16 | 33/25 | 22/34 | 11/37 | 176/176 | |
11/20 | 22/13 | 33/15 | 44/24 | 33/35 | 22/38 | 11/31 | 176/176 | |
11/30 | 22/20 | 33/14 | 44/16 | 33/25 | 22/34 | 11/37 | 176/176 | |
11/30 | 22/20 | 33/14 | 44/16 | 33/25 | 22/34 | 11/37 | 176/176 | |
11/20 | 22/13 | 33/15 | 44/24 | 33/35 | 22/38 | 11/31 | 176/176 | |
11/30 | 22/20 | 33/14 | 44/16 | 33/25 | 22/34 | 11/37 | 176/176 | |
11/32 | 22/26 | 33/19 | 44/17 | 33/21 | 22/28 | 11/33 | 176/176 | |
11/26 | 22/18 | 33/16 | 44/20 | 33/29 | 22/34 | 11/33 | 176/176 | |
11/32 | 22/26 | 33/19 | 44/17 | 33/21 | 22/28 | 11/33 | 176/176 | |
132/340 | 264/246 | 396/194 | 528/220 | 396/312 | 264/392 | 132/408 | 2112/2112 | |
. 5 , ᒺ , d, , , ᒺ , d, . , , 8 (15) 5 8, 7 8, 9 8, 11 8 (4 2 = 8), 2 8, 4 8, 6 8, 10 8, 12 8 (5 1 = 5) 1 8, 3 8 (2 1 = 2).
. 6 ᒺ , ( / ).
6 ᒺ
ij | ||||||||
1 2/ 2 1 | 11/26 | 22/19 | 33/17 | 44/21 | 33/28 | 22/33 | 11/32 | 176/176 |
2 3/3 2 | 26/11 | 19/22 | 17/33 | 21/44 | 28/33 | 33/22 | 32/11 | 176/176 |
2 5/5 2 | 27/48 | 36/36 | 63/42 | 90/63 | 99/84 | 72/87 | 45/72 | 432/432 |
4 5/5 4 | 11/20 | 22/14 | 33/16 | 44/25 | 33/34 | 22/37 | 11/30 | 176/176 |
5 6/6 5 | 20/11 | 14/22 | 16/33 | 25/44 | 34/33 | 37/22 | 30/11 | 176/176 |
5 8/8 5 | 48/48 | 42/42 | 66/66 | 102/102 | 126/126 | 114/114 | 78/78 | 576/576 |
7 8/8 7 | 11/20 | 22/14 | 33/16 | 44/25 | 33/34 | 22/37 | 11/30 | 176/176 |
8 9/9 8 | 20/11 | 14/22 | 16/33 | 25/44 | 34/33 | 37/22 | 30/11 | 176/176 |
8 11/11 8 | 48/27 | 36/36 | 42/63 | 63/90 | 84/99 | 87/72 | 72/45 | 432/432 |
10 11/11 10 | 11/26 | 22/19 | 33/17 | 44/21 | 33/28 | 22/33 | 11/32 | 176/176 |
11 12/12 11 | 26/11 | 19/22 | 17/33 | 21/44 | 28/33 | 33/22 | 32/11 | 176/176 |
259/259 | 268/268 | 369/369 | 523/523 | 565/565 | 501/501 | 363/363 | 2848/2848 | |
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. 6 , ᒺ , , , .
, , . , 11 8 (90) 11 1, 2,..., 9 (9 4 = 36) 10, 12 1, 2,..., 9 (18 3 = 54).
.
. 6.
. 7 1/2 .
7 1/2
ij | / | ||||||
2 5 | 0/27 | 1/36 | 2/63 | 3/90 | 4/99 | 5/72 | 6/45 |
5 8 | 1/42 | 2/66 | 3/102 | 4/126 | 5/114 | 6/78 | 0/48 |
8 11 | 2/42 | 3/63 | 4/84 | 5/87 | 6/72 | 0/48 | 1/36 |
11 8 | 3/90 | 4/99 | 5/72 | 6/45 | 0/27 | 1/36 | 2/63 |
8 5 | 4/126 | 5/114 | 6/78 | 0/48 | 1/42 | 2/66 | 3/102 |
5 2 | 5/87 | 6/72 | 0/48 | 1/36 | 2/42 | 3/63 | 4/84 |
4/126 | 5/114 | 3/102 | 4/126 | 5/114 | 6/78 | 3/102 |
. 7 , (126) , ( ) ( ), , , 8 5 , , , 5 8 .
ϳ, 36 4 = 144.