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q
403.1999969 0 0 336.9600067 0 239.0399933 cm
/Im0 Do
Q
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403.1999969 0 0 239.0399933 0 0 cm
/Im1 Do
Q
BT
/T1_0 1 Tf
0.05 Tc 3 Tr 10.0387 0 0 8.8 32.7 531.73 Tm
(Example )Tj
9.1783 0 0 8.8 75.13 531.73 Tm
(3.12 )Tj
/T1_1 1 Tf
0 Tc 8.5 0 0 8.5 98.89 531.73 Tm
(K)Tj
/T1_2 1 Tf
-0.035 Tc 5.8569 0 0 6 106.64 530.65 Tm
(12)Tj
-0.0239 Tc 6 0 0 6 113.24 531.73 Tm
(,12 )Tj
/T1_0 1 Tf
0.017 Tc 9 0 0 9 124.11 531.73 Tm
(can )Tj
0.0066 Tc 1.771 0 Td
(be )Tj
-0.0042 Tc 1.353 0 Td
(2-factorized )Tj
0.0207 Tc 5.138 0 Td
(into )Tj
/T1_3 1 Tf
0 Tc 22.4 0 0 22.4 216.13 531.73 Tm
(\260 )Tj
/T1_0 1 Tf
-0.0326 Tc 9 0 0 9 223.83 531.73 Tm
(or )Tj
-0.035 Tc 8.8631 0 0 9 234.41 531.73 Tm
(18 )Tj
-0.0054 Tc 9 0 0 9 246.08 531.73 Tm
(8-cycles. )Tj
0.05 Tc 9.9428 0 0 9 32.9 520.21 Tm
(Proof: )Tj
-0.032 Tc 9 0 0 9 69.73 520.21 Tm
(\(i\) )Tj
/T1_3 1 Tf
0 Tc 22.4 0 0 22.4 81.13 520.21 Tm
(\260 )Tj
7.1 0 0 7.1 88.58 520.21 Tm
(E )Tj
/T1_1 1 Tf
0.05 Tc 9.7427 0 0 9.1 96.58 520.21 Tm
(Q\(K)Tj
/T1_2 1 Tf
-0.035 Tc 5.8569 0 0 6 115.1 519.85 Tm
(12)Tj
0.05 Tc 6.3919 0 0 6 121.34 520.21 Tm
(,12\): )Tj
/T1_0 1 Tf
0.0202 Tc 9 0 0 9 46 510.31 Tm
(Take )Tj
0 Tc 2.419 0 Td
(a )Tj
0.0283 Tc 0.826 0 Td
(Hamilton )Tj
0.0072 Tc 4.336 0 Td
(decomposition )Tj
0.0074 Tc 6.319 0 Td
(of )Tj
/T1_1 1 Tf
0 Tc 8.8 0 0 8.8 181.15 510.31 Tm
(K)Tj
/T1_2 1 Tf
-0.035 Tc 5.6617 0 0 6 188.72 509.05 Tm
(12)Tj
0.05 Tc 6.0078 0 0 6 194.78 510.31 Tm
(,12. )Tj
/T1_0 1 Tf
0.0063 Tc 9 0 0 9 46.69 499.51 Tm
(\(ii\) )Tj
-0.035 Tc 8.4602 0 0 9 61.81 499.51 Tm
(18 )Tj
/T1_3 1 Tf
0 Tc 7.1 0 0 7.1 73.1 499.51 Tm
(E )Tj
/T1_1 1 Tf
0.05 Tc 9.5478 0 0 9.1 81.1 499.51 Tm
(Q\(K)Tj
/T1_2 1 Tf
-0.035 Tc 5.8569 0 0 6 99.26 498.43 Tm
(12)Tj
0.05 Tc 6.3919 0 0 6 105.68 499.51 Tm
(,12\): )Tj
/T1_0 1 Tf
9.0143 0 0 9 46.39 489.43 Tm
(Let )Tj
9.0033 0 0 9 61.91 489.43 Tm
({I, )Tj
-0.035 Tc 8.5333 0 0 9 74.65 489.43 Tm
(2, )Tj
8.4944 0 0 9 83.06 489.43 Tm
(3, )Tj
8.2321 0 0 9 91.41 489.43 Tm
(4, )Tj
8.4607 0 0 9 99.78 489.43 Tm
(5, )Tj
8.8645 0 0 9 108.07 489.43 Tm
(6, )Tj
8.3431 0 0 9 116.73 489.43 Tm
(7, )Tj
-0.0349 Tc 9 0 0 9 124.76 489.43 Tm
(8, )Tj
0.0336 Tc 0.947 0 Td
(9,10,11, )Tj
-0.035 Tc 8.7471 0 0 9 166.74 489.43 Tm
(12} )Tj
0.004 Tc 9 0 0 9 180.99 489.43 Tm
(and )Tj
-0.0155 Tc 1.729 0 Td
({13, )Tj
0.05 Tc 9.0528 0 0 9 214.25 489.43 Tm
(14,15,16,17,18,19,20,21,22,23, )Tj
-0.035 Tc 8.2872 0 0 9 342.67 489.43 Tm
(24} )Tj
0.0266 Tc 9 0 0 9 33.13 478.63 Tm
(be )Tj
0.05 Tc 9.2893 0 0 9 45.34 478.63 Tm
(the )Tj
0.0418 Tc 9 0 0 9 61.57 478.63 Tm
(parts )Tj
0.0074 Tc 2.509 0 Td
(of )Tj
/T1_1 1 Tf
0 Tc 8.8 0 0 8.8 94.39 478.63 Tm
(K)Tj
-0.035 Tc 5.3495 0 0 5.8001 102.01 477.19 Tm
(12)Tj
0.0449 Tc 5.8001 0 0 5.8001 108.5 478.63 Tm
(,12' )Tj
/T1_0 1 Tf
0.0317 Tc 9 0 0 9 123.94 478.63 Tm
(The )Tj
-0.0231 Tc 2.018 0 Td
(following )Tj
0.001 Tc 4.106 0 Td
(2-factors )Tj
-0.0207 Tc 3.954 0 Td
(form )Tj
0 Tc 2.321 0 Td
(a )Tj
0.0286 Tc 0.884 0 Td
(2-factorization )Tj
0.0074 Tc 6.656 0 Td
(of )Tj
/T1_3 1 Tf
0 Tc 8.5 0 0 8.5 313.74 478.63 Tm
(K)Tj
/T1_0 1 Tf
-0.035 Tc 5.8416 0 0 6 321.28 477.37 Tm
(12)Tj
-0.0244 Tc 6 0 0 6 327.51 478.63 Tm
(,12 )Tj
-0.035 Tc 8.9404 0 0 9 338.67 478.63 Tm
(con\255)Tj
0.0481 Tc 9 0 0 9 33.1 467.65 Tm
(taining )Tj
-0.035 Tc 8.6617 0 0 9 63.78 467.65 Tm
(18 )Tj
-0.0154 Tc 9 0 0 9 75.26 467.65 Tm
(8-cycles. )Tj
0.05 Tc 9.122 0 0 9 33.62 456.85 Tm
([\(1,13,2,14,3,15,4,16\), )Tj
0.0397 Tc 9 0 0 9 128.59 456.85 Tm
(\(9,21,10,22,11,23,12,24\), )Tj
0.05 Tc 9.1888 0 0 9 231.19 456.85 Tm
(\(5,17,6,18,7,19,8,20\)]' )Tj
9.122 0 0 9 33.62 445.87 Tm
([\(1,14,4,13,3,16,2,15\), )Tj
-0.035 Tc 8.6913 0 0 9 128.42 445.87 Tm
(\(5, )Tj
0.0482 Tc 9 0 0 9 139.73 445.87 Tm
(18,8,17,7,20,6,19\), )Tj
0.0492 Tc 8.742 0 Td
(\(9,22,12,21,11,24,10,23\)]' )Tj
0.05 Tc 9.1041 0 0 9 33.8 435.25 Tm
([\(1,17,2,18,3,19,4,20\), )Tj
0.0482 Tc 9 0 0 9 128.59 435.25 Tm
(\(5,21,6,22,7,23,8,24\), )Tj
0.0464 Tc 10 0 Td
(\(9,13,10,14,11,15,12,16\)], )Tj
0.05 Tc 9.1041 0 0 9 33.98 424.63 Tm
([\(1,18,4,17,3,20,2,19\), )Tj
0.0473 Tc 9 0 0 9 128.77 424.63 Tm
(\(5,22,8,21,7,24,6,23\), )Tj
0.0484 Tc 10 0 Td
(\(9,14,12,13,11,16,10,15\)]' )Tj
0.05 Tc 9.1041 0 0 9 33.98 413.65 Tm
([\(1,21,2,22,3,23,4,24\), )Tj
0.0473 Tc 9 0 0 9 128.77 413.65 Tm
(\(5,13,6,14,7,15,8,16\), )Tj
0.0484 Tc 10 0 Td
(\(9,17,10,18,11,19,12,20\)]' )Tj
0.05 Tc 9.1041 0 0 9 34.16 402.67 Tm
([\(1,22,4,21,3,24,2,23\), )Tj
-0.035 Tc 8.5103 0 0 9 128.96 402.67 Tm
(\(5, )Tj
0.0482 Tc 9 0 0 9 140.09 402.67 Tm
(14,8,13,7,16,6,15\), )Tj
0.044 Tc 8.762 0 Td
(\(9,18,12,17,11,20,10,19\)]. )Tj
0.05 Tc 9.9449 0 0 8.8 33.96 378.73 Tm
(Example )Tj
9.0817 0 0 8.8 76.21 378.73 Tm
(3.13 )Tj
/T1_2 1 Tf
-0.0123 Tc 9.3 0 0 9.3 99.77 378.73 Tm
(Q\(39\) )Tj
/T1_0 1 Tf
0 Tc 10.5 0 0 10.5 125.41 378.73 Tm
(= )Tj
/T1_2 1 Tf
0.009 Tc 9.3 0 0 9.3 134.71 378.73 Tm
(FC\(39\). )Tj
/T1_0 1 Tf
0.05 Tc 9.8769 0 0 9 33.98 367.74 Tm
(Proof: )Tj
-0.035 Tc 9.273 0 0 9.5 75.67 367.74 Tm
(\(i\) )Tj
-0.0065 Tc 9 0 0 9 88.48 367.74 Tm
(Take )Tj
/T1_2 1 Tf
0 Tc 9.4 0 0 9.4 111.01 367.74 Tm
(r )Tj
/T1_3 1 Tf
8.1 0 0 8.1 119.75 367.74 Tm
(= )Tj
/T1_0 1 Tf
-0.035 Tc 8.4944 0 0 9 131.12 367.74 Tm
(3, )Tj
/T1_2 1 Tf
0 Tc 10 0 0 10 141.9 367.74 Tm
(t )Tj
/T1_3 1 Tf
8.1 0 0 8.1 149.63 367.74 Tm
(= )Tj
/T1_0 1 Tf
9 0 0 9 160.82 367.74 Tm
(3 )Tj
0.014 Tc 0.901 0 Td
(and )Tj
/T1_2 1 Tf
0 Tc 9.4 0 0 9.4 186.78 367.74 Tm
(v )Tj
/T1_3 1 Tf
8.1 0 0 8.1 195.53 367.74 Tm
(= )Tj
/T1_0 1 Tf
-0.035 Tc 8.8631 0 0 9 206.87 367.74 Tm
(12 )Tj
8.6795 0 0 9 220.07 367.74 Tm
(in )Tj
0.0381 Tc 9 0 0 9 231.03 367.74 Tm
(Construction )Tj
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(A. )Tj
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(FC\(39\) )Tj
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(\\ )Tj
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({76} )Tj
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<007E0020>Tj
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(Q\(39\). )Tj
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(\(ii\) )Tj
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(The )Tj
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(2-factorization )Tj
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(of )Tj
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(\(20,26,23,24,21,27,22,25\)]' )Tj
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([\(1,6,2,4,5,3, )Tj
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(7\),\(8,10,9,11,39,37,38,36\),\(12,14,13,15,35,33,34,32\), )Tj
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(\(20,22,21,23,27,25,26,24\)], )Tj
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([\(1,8,3,10,11,2,9\),\(12,38,15,36,13,39,14,37\),\(16,34,19,32,17,35,18,\
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(\(20,30,23,28,21,31,22,29\), )Tj
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(\(4,26,7,24,6,27,5,25\)]' )Tj
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([\(1, )Tj
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(17,33,19,35\), )Tj
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(\(20,28,22,30,21,29,23,31\),\(4,24,5,26,6,25,7,27\)]' )Tj
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([\(1, )Tj
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(12,3,14,15,2,13\),\(16,38,19,36,17,39,18,37\),\(20,34,23,32,21,35,22,33\)\
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(\(24,30,27,28,25,31,26,29\), )Tj
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(\(4,10,7,8,6,11,5,9\)]' )Tj
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([\(1,14,2,12,13,3,15\),\(16,36,18,38,17,37,19,39\),\(20,32,22,34,21,33,2\
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(\(24,28,26,30,25,29,27,31\), )Tj
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(\(4,8,5,10,6,9,7,11\)]' )Tj
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([\(1, )Tj
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(16,3, )Tj
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(18, )Tj
8.7679 0 0 9 83.94 206.65 Tm
(19, )Tj
8.2747 0 0 9 96.61 206.65 Tm
(2, )Tj
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(17\), )Tj
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(\(8, )Tj
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(14, )Tj
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(11, )Tj
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(12,9,15,10,13\), )Tj
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(\(20,38,23,36,21,39,22,37\), )Tj
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(\(24,34,27,32,25,35,26,33\), )Tj
0.045 Tc 12.16 0 Td
(\(4,30,7,28,6,31,5,29\)]' )Tj
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([\(1,18,2,16,17,3,19\), )Tj
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(\(8,12,10,14,9,13,11,15\), )Tj
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(\(20,36,22,38,21,37,23,39\), )Tj
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(\(24,32,26,34,25,33,27,35\), )Tj
0.045 Tc 12.16 0 Td
(\(4,28,5,30,6,29,7,31\)]' )Tj
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([\(1,20,3,22,23,2,21\), )Tj
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(\(8, )Tj
8.7679 0 0 9 133.44 163.99 Tm
(18, )Tj
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(11, )Tj
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(16,9,19,10,17\), )Tj
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(\(4,14,7,12,6, )Tj
0.0461 Tc 5.998 0 Td
(15,5,13\), )Tj
0.0469 Tc -26.518 -1.18 Td
(\(24,38,27,36,25,39,26,37\), )Tj
0.0381 Tc 12.14 0 Td
(\(28,34,31,32,29,35,30,33\)]' )Tj
0.05 Tc 9.1793 0 0 9 35.78 142.93 Tm
([\(1,22,2,20,21,3,23\),\(8,16,10,18,9,17,11,19\),\(4,12,5,14,6,13,7,15\)\
, )Tj
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(\(24,36,26,38,25,37,27,39\), )Tj
0.0354 Tc 12.14 0 Td
(\(28,32,30,34,29,33,31,35\)], )Tj
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([\(1,24,3,26,27,2,25\), )Tj
0.044 Tc 9 0 0 9 122.47 121.32 Tm
(\(8,22,11,20,9,23,10,21\), )Tj
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(\(12, )Tj
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(18, )Tj
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(15, )Tj
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(16, )Tj
0.0382 Tc 1.48 0 Td
(13,19,14,17\), )Tj
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(\(28,38,31,36,29,39,30,37\), )Tj
0.045 Tc 12.16 0 Td
(\(4,34,7,32,6,35,5,33\)]' )Tj
0.05 Tc 9.0771 0 0 9 36.5 99.36 Tm
([\(1,26,2,24,25,3,27\),\(8,20,10,22,9,21,11,23\),\(12,16,14,18,13,17,15,\
19\), )Tj
9.0344 0 0 9 36.79 88.74 Tm
(\(28,36,30,38,29,37,31,39\),\(4,32,5,34,6,33,7,35\)]' )Tj
9.0771 0 0 9 36.5 77.95 Tm
([\(1,28,3,30,31,2,29\),\(8,26,11,24,9,27,10,25\),\(12,22,15,20,13,23,14,\
21\), )Tj
0.0461 Tc 9 0 0 9 36.79 67.14 Tm
(\(32,38,35,36,33,39,34,37\), )Tj
0.0459 Tc 12.14 0 Td
(\(4,18,7,16,6,19,5,17\)]' )Tj
-0.035 Tc 8.8017 0 0 9 190.03 36.37 Tm
(217 )Tj
ET
endstream
endobj
324 0 obj
<>/Filter/CCITTFaxDecode/Height 1872/Length 44249/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream
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