Generate all combinations in SQL

Question

I need to generate all combinations of size @k in a given set of size @n. Can someone please review the following SQL and determine first if the fo

Answer 1

Please forgive this extra answer. I ran into the post character limit in my original answer.

Here are the complete averaged numeric performance results for the charts in my answer.

      |             Erik             |             Peter
 N  K |  CPU  Duration Reads  Writes |  CPU  Duration  Reads  Writes
-- -- - ----- -------- ------ ------ - ----- -------- ------- ------
 1  1 |     0        0      7      0 |     0        0       7      0
 2  1 |     0        0     10      0 |     0        0       7      0
 2  2 |     0        0      7      0 |     0        0      11      0
 3  1 |     0        0     12      0 |     0        0       7      0
 3  2 |     0        0     12      0 |     0        0      13      0
 3  3 |     5        0      7      0 |     0        0      19      0
 4  1 |     0        0     14      0 |     0        0       7      0
 4  2 |     0        0     18      0 |     0        0      15      0
 4  3 |     0        0     14      0 |     5        0      27      0
 4  4 |     0        0      7      0 |     0        0      35      0
 5  1 |     5        0     16      0 |     5        0       7      0
 5  2 |     0        0     26      0 |     0        0      17      0
 5  3 |     0        0     26      0 |     0        0      37      0
 5  4 |     0        0     16      0 |     0        0      57      0
 5  5 |     0        0      7      0 |     0        0      67      0
 6  1 |     0        0     18      0 |     0        0       7      0
 6  2 |     5        0     36      0 |     0        0      19      0
 6  3 |     0        0     46      0 |     0        0      49      0
 6  4 |     0        0     36      0 |     0        0      89      0
 6  5 |     5        0     18      0 |     5        0     119      0
 6  6 |     0        0      7      0 |     0        0     131      0
 7  1 |     5        0     20      0 |     0        0       7      0
 7  2 |     0        0     48      0 |     0        0      21      0
 7  3 |     0        0     76      0 |     0        0      63      0
 7  4 |     0        0     76      0 |     0        0     133      0
 7  5 |     0        1     48      0 |     0        1     203      0
 7  6 |     5        0     20      0 |     0        1     245      0
 7  7 |     5        0      7      0 |     0        3     259      0
 8  1 |     5        2     22      0 |     0        4       7      0
 8  2 |     0        1     62      0 |     0        0      23      0
 8  3 |     0        1    118      0 |     0        0      79      0
 8  4 |     0        1    146      0 |     0        1     191      0
 8  5 |     5        3    118      0 |     0        1     331      0
 8  6 |     5        1     62      0 |     5        2     443      0
 8  7 |     0        0     22      0 |     5        3     499      0
 8  8 |     0        0      7      0 |     5        3     515      0
 9  1 |     0        2     24      0 |     0        0       7      0
 9  2 |     5        3     78      0 |     0        0      25      0
 9  3 |     5        3    174      0 |     0        1      97      0
 9  4 |     5        5    258      0 |     0        2     265      0
 9  5 |     5        7    258      0 |    10        4     517      0
 9  6 |     5        5    174      0 |     5        5     769      0
 9  7 |     0        3     78      0 |    10        4     937      0
 9  8 |     0        0     24      0 |     0        3    1009      0
 9  9 |     0        1      7      0 |     0        4    1027      0
10  1 |    10        4     26      0 |     0        0       7      0
10  2 |     5        5     96      0 |     0        0      27      0
10  3 |     5        2    246      0 |     0        0     117      0
10  4 |    10       10    426      0 |    10        4     357      0
10  5 |    15       12    510      0 |     5        8     777      0
10  6 |    15       16    426      0 |    10        9    1281      0
10  7 |    10        4    246      0 |    10        9    1701      0
10  8 |    10        5     96      0 |    10        5    1941      0
10  9 |     5        4     26      0 |    10        7    2031      0
10 10 |     5        0      7      0 |    10        7    2051      0
11  1 |    10        8     28      0 |     0        0       7      0
11  2 |    15       11    116      0 |     0        0      29      0
11  3 |    21       24    336      0 |    10        3     139      0
11  4 |    21       18    666      0 |     5        2     469      0
11  5 |    21       20    930      0 |     5        3    1129      0
11  6 |    26       35    930      0 |    15       12    2053      0
11  7 |    20       14    666      0 |     5       25    2977      0
11  8 |    15        9    336      0 |    20       14    3637      0
11  9 |    10        7    116      0 |    21       27    3967      0
11 10 |    10        8     28      0 |    36       34    4086      0
11 11 |     5        8      7      0 |    15       15    4109      0
12  1 |    16       18     30      0 |     5        0       7      0
12  2 |    31       32    138      0 |     0        0      31      0
12  3 |    31       26    446      0 |    10        2     163      0
12  4 |    47       40    996      0 |    10        7     603      0
12  5 |    47       46   1590      0 |    21       17    1593      0
12  6 |    57       53   1854      0 |    31       30    3177      0
12  7 |    41       39   1590      0 |    31       30    5025      0
12  8 |    41       42    996      0 |    42       43    6609      0
12  9 |    31       26    446      0 |    52       52    7607      0
12 10 |    20       19    138      0 |    57       62    8048      0
12 11 |    15       17     30      0 |    72       64    8181      0
12 12 |    15       10      7      0 |    67       38    8217      0
13  1 |    31       32     32      0 |     0        0       7      0
13  2 |    21       25    162      0 |     0        0      33      0
13  3 |    36       34    578      0 |     5        2     189      0
13  4 |    57       65   1436      0 |    10        5     761      0
13  5 |    41       40   2580      0 |    10       10    2191      0
13  6 |    62       56   3438      0 |    31       32    4765      0
13  7 |    62       62   3438      0 |    57       53    8251      0
13  8 |    52       64   2580      0 |    52       47   11710      0
13  9 |    26       28   1436      0 |    93       96   14311      0
13 10 |    31       29    578      0 |   161      104   15891      0
13 11 |    36       35    162      0 |   129       99   16525      0
13 12 |    21       22     32      0 |   156       96   16383      0
13 13 |    26       30      7      0 |   166       98   16411      0
14  1 |    57       53     34      0 |     0        0       7      0
14  2 |    52       50    188      0 |     0        0      35      0
14  3 |    57       60    734      0 |    10        4     217      0
14  4 |    78       76   2008      0 |    15        8     945      0
14  5 |    99       97   4010      0 |    36       34    2947      0
14  6 |   120      125   6012      0 |    41       47    6951      0
14  7 |   125      119   6870      0 |    93       94   12957      0
14  8 |   135      138   6012      0 |    88       98   19821      0
14  9 |    78      153   4010      0 |   234      156   26099      0
14 10 |    94       92   2008      0 |   229      133   30169      0
14 11 |    83       90    734      0 |   239      136   32237      0
14 12 |    47       46    188      0 |   281      176   33031      0
14 13 |    52       53     34      0 |   260      167   32767      0
14 14 |    46       47      7      0 |   203      149   32797      0
15  1 |    83       83     36      0 |     0        0       7      0
15  2 |   145      139    216      0 |     0        2      37      0
15  3 |   104       98    916      0 |     0        2     247      0
15  4 |   135      135   2736      0 |    15       17    1157      0
15  5 |    94       97   6012      0 |    26       27    3887      0
15  6 |   192      188  10016      0 |    57       53    9893      0
15  7 |   187      192  12876      0 |    73       73   19903      0
15  8 |   286      296  12876      0 |   338      230   33123      0
15  9 |   208      207  10016      0 |   354      223   46063      0
15 10 |   140      143   6012      0 |   443      334   56143      0
15 11 |    88       86   2736      0 |   391      273   62219      0
15 12 |    73       72    916      0 |   432      269   65019      0
15 13 |   109      117    216      0 |   317      210   65999      0
15 14 |   156      187     36      0 |   411      277   66279      0
15 15 |   140      142      7      0 |   354      209   65567      0
16  1 |   281      281     38      0 |     0        0       7      0
16  2 |   141      146    246      0 |     0        0      39      0
16  3 |   208      206   1126      0 |    10        4     279      0
16  4 |   187      189   3646      0 |    15       13    1399      0
16  5 |   234      234   8742      0 |    42       42    5039      0
16  6 |   333      337  16022      0 |    83       85   13775      0
16  7 |   672      742  22886      0 |   395      235   30087      0
16  8 |   510      510  25746      0 |   479      305   53041      0
16  9 |   672      675  22886      0 |   671      489   78855      0
16 10 |   489      492  16022      0 |   859      578  101809      0
16 11 |   250      258   8742      0 |   719      487  117899      0
16 12 |   198      202   3646      0 |   745      483  126709      0
16 13 |   119      119   1126      0 |   770      506  130423      0
16 14 |   291      327    246      0 |   770      531  131617      0
16 15 |   156      156     38      0 |   713      451  131931      0
16 16 |   125      139      7      0 |   895      631  132037      0
17  1 |   406      437     40      0 |     0        0       7      0
17  2 |   307      320    278      0 |     0        0      41      0
17  3 |   281      290   1366      0 |     0        3     313      0
17  4 |   307      317   4766      0 |    31       28    1673      0
17  5 |   354      378  12382      0 |    41       45    6433      0
17  6 |   583      582  24758      0 |   130      127   18809      0
17  7 |   839      859  38902      0 |   693      449   43873      0
17  8 |  1177     1183  48626      0 |   916      679   82847      0
17  9 |  1031     1054  48626      0 |  1270      944  131545      0
17 10 |   828      832  38902      0 |  1469     1105  180243      0
17 11 |   672      668  24758      0 |  1535     1114  219217      0
17 12 |   422      422  12382      0 |  1494      991  244047      0
17 13 |   474      482   4766      0 |  1615     1165  256501      0
17 14 |   599      607   1366      0 |  1500     1042  261339      0
17 15 |   223      218    278      0 |  1401     1065  262777      0
17 16 |   229      228     40      0 |  1390      918  263127      0
17 17 |   541      554      7      0 |  1562     1045  263239      0
18  1 |   401      405     42      0 |     0        0       7      0
18  2 |   401      397    312      0 |     0        0      43      0
18  3 |   458      493   1638      0 |     5        6     349      0
18  4 |   583      581   6126      0 |    16       13    1981      0
18  5 |   697      700  17142      0 |    83      130    8101      0
18  6 |   792      799  37134      0 |   156      162   25237      0
18  7 |  1672     1727  63654      0 |  1098      751   62693      0
18  8 |  1598     1601  87522      0 |  1416     1007  126423      0
18  9 |  1849     1893  97246      0 |  2051     1522  214021      0
18 10 |  1963     2083  87522      0 |  2734     2103  311343      0
18 11 |  1411     1428  63654      0 |  2849     2352  398941      0
18 12 |  1042     1048  37134      0 |  3021     2332  462671      0
18 13 |   942      985  17142      0 |  3036     2314  499881      0
18 14 |   656      666   6126      0 |  3052     2177  517099      0
18 15 |   526      532   1638      0 |  2910     2021  523301      0
18 16 |   614      621    312      0 |  3083     2108  525015      0
18 17 |   536      551     42      0 |  2921     2031  525403      0
18 18 |   682      680      7      0 |  3141     2098  525521      0
19  1 |   885      909     44      0 |     0        0       7      0
19  2 |  1411     1498    348      0 |     0        0      45      0
19  3 |   880      887   1944      0 |     5        4     387      0
19  4 |  1119     1139   7758      0 |    26       25    2325      0
19  5 |  1120     1127  23262      0 |    73       72   10077      0
19  6 |  1395     1462  54270      0 |   453      387   33591      0
19  7 |  1875     1929 100782      0 |  1197      838   87941      0
19  8 |  2656     2723 151170      0 |  2255     1616  188803      0
19  9 |  3046     3092 184762      0 |  3317     2568  340053      0
19 10 |  3635     3803 184762      0 |  5171     4041  524895      0
19 11 |  2739     2774 151170      0 |  5577     4574  709737      0
19 12 |  3203     3348 100782      0 |  6182     5194  860987      0
19 13 |  1672     1750  54270      0 |  6458     5561  961849      0
19 14 |  1760     1835  23262      0 |  6177     4964 1016199      0
19 15 |   968     1006   7758      0 |  6266     4331 1039541      0
19 16 |  1099     1134   1944      0 |  6208     4254 1047379      0
19 17 |   995     1037    348      0 |  6385     4366 1049403      0
19 18 |   916      964     44      0 |  6036     4268 1049831      0
19 19 |  1135     1138      7      0 |  6234     4320 1049955      0
20  1 |  1797     1821     46      0 |     0        0       7      0
20  2 |  2000     2029    386      0 |     0        0      47      0
20  3 |  2031     2071   2286      0 |    10        6     427      0
20  4 |  1942     2036   9696      0 |    31       34    2707      0
20  5 |  2104     2161  31014      0 |    88       85   12397      0
20  6 |  2880     2958  77526      0 |   860      554   43675      0
20  7 |  3791     3940 155046      0 |  2026     1405  121285      0
20  8 |  5130     5307 251946      0 |  3823     2731  276415      0
20  9 |  6547     6845 335926      0 |  5380     4148  528445      0
20 10 |  7119     7357 369518      0 |  8271     6685  864455      0
20 11 |  5692     5803 335926      0 |  9557     8029 1234057      0
20 12 |  4734     4850 251946      0 | 11114     9504 1570067      0
20 13 |  3604     3641 155046      0 | 11551    10434 1822097      0
20 14 |  2911     2999  77526      0 | 12317    10822 1977227      0
20 15 |  2115     2134  31014      0 | 12806    10679 2054837      0
20 16 |  2041     2095   9696      0 | 13062     9115 2085935      0
20 17 |  2390     2465   2286      0 | 12807     9002 2095715      0
20 18 |  1765     1788    386      0 | 12598     8601 2098085      0
20 19 |  2067     2143     46      0 | 12578     8626 2098555      0
20 20 |  1640     1663      7      0 | 12932     9064 2098685      0
21  1 |  3374     3425     48      0 |     0        0       7      0
21  2 |  4031     4157    426      0 |     0        1      49      0
21  3 |  3218     3250   2666      0 |    10        5     469      0
21  4 |  3687     3734  11976      0 |    21       25    3129      0
21  5 |  3692     3735  40704      0 |   115      114   15099      0
21  6 |  4859     4943 108534      0 |   963      661   56079      0
21  7 |  6114     6218 232566      0 |  2620     1880  164701      0
21  8 |  8573     8745 406986      0 |  4999     3693  397355      0
21  9 | 11880    12186 587866      0 |  9047     6863  804429      0
21 10 | 13255    13582 705438      0 | 14358    11436 1392383      0
21 11 | 13531    13807 705438      0 | 18823    15502 2097909      0
21 12 | 12244    12400 587866      0 | 21834    18760 2803435      0
21 13 |  9406     9528 406986      0 | 23771    21274 3391389      0
21 14 |  7114     7180 232566      0 | 26677    24296 3798463      0
21 15 |  4869     4961 108534      0 | 26479    23998 4031117      0
21 16 |  4416     4521  40704      0 | 26536    22976 4139739      0
21 17 |  4380     4443  11976      0 | 26490    19107 4180531      0
21 18 |  3265     3334   2666      0 | 25979    17995 4192595      0
21 19 |  3640     3768    426      0 | 26186    17891 4195349      0
21 20 |  3234     3295     48      0 | 25688    17653 4195863      0
21 21 |  3156     3219      7      0 | 26140    17838 4195999      0