Cycle types and frequency in Enriched Schubert problems in G(4,9)

 Non reduced problems are highlighted with this background color 
Schubert problems fibered over 4=2 on Gr(2,4)
Fiber ˙4 ˙3 2˙2 ˙4 6
Galois Group S2WrS2 S2WrS2 S2WrS2 S3WrS2 S5WrS2
Number212026219

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Schubert problems fibered over 4=2 on Gr(2,4) with Galois group S2WrS2 of order 8
Fiber: 2 = ˙˙˙˙ 
Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)
       12422 18697 12256 6161
       12490 18460 12409 6137
       12348 18724 12333 6095
        12246 18738 12322 6266
        12434 18514 12285 6265
        12447 18595 12486 6084
        12395 18731 12248 6174
        12500 18580 12334 6128
        12504 18462 12312 6267
         12459 18479 12522 6087
         12308 18539 12501 6261
         12239 18704 12431 6165
         12506 18417 12480 6132
         12526 18458 12327 6174
         12397 18532 12545 6071
         12654 18515 12276 6134
          12554 18613 12227 6214
          12495 18345 12368 6333
          12500 18557 12353 6148
          12307 18719 12303 6219
           12639 18419 12399 6136
Fiber: 2 = ˙˙˙ 
Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)
       12377 18560 12429 6143
       12628 18505 12173 6245
        12276 18475 12524 6237
      12580 18408 12347 6132
      12453 18635 12284 6144
       12263 18639 12406 6238
       12452 18385 12467 6203
       12629 18638 12084 6232
       12409 18651 12295 6167
        12420 18504 12546 6141
        12245 18523 12574 6167
        12506 18528 12472 6084
        12462 18614 12298 6117
        12543 18526 12255 6228
        12301 18636 12494 6075
         12638 18458 12258 6263
         12370 18629 12295 6255
         12329 18531 12402 6318
         12491 18392 12436 6228
          12540 18368 12439 6176
Fiber: 2 = ˙˙˙ 
Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)
      12516 18450 12409 6195
      12448 18464 12419 6173
      12294 18641 12216 6343
       12397 18564 12434 6167
       12330 18646 12316 6216
       12403 18556 12254 6338
       12634 18494 12315 6154
       12486 18652 12126 6246
       12427 18734 12355 6027
       12204 18712 12396 6213
       12317 18417 12604 6181
        12473 18592 12283 6215
        12427 18378 12605 6159
        12271 18588 12475 6150
        12445 18473 12556 6057
        12278 18465 12530 6213
        12371 18523 12410 6223
        12476 18505 12467 6133
        12493 18603 12328 6108
        12514 18454 12496 6104
        12440 18547 12285 6277
         12516 18485 12404 6161
         12474 18755 12301 6078
         12482 18674 12142 6230
         12518 18439 12446 6130
          12392 18568 12381 6175

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These are all fibered over 4=2 in Gr(2,4) with fiber ˙4=3 in Gr(2,5).
These have the same Galois group, S3WrS2, which has order 72
Schubert Problem (6) (4,2) (3,3) (3,2,1) (3,1,1,1) (2,2,2) (2,2,1,1) (2,1,1,1,1) (1,1,1,1,1,1)
       8294 12324 2747 8240 2797 4165 6222 4061 665
       8286 12526 2659 8105 2627 4270 6251 4095 666
       8122 12511 2638 8291 2683 4211 6210 4167 686
        8341 12545 2740 8130 2673 4116 6120 4163 674
        8316 12325 2654 8159 2794 4182 6255 4125 681
        8453 12221 2727 8258 2704 4196 6206 4089 689
        8028 12345 2762 8194 2746 4227 6314 4276 673
        8301 12519 2708 8118 2768 4107 6168 4109 683
        8207 12497 2740 8167 2779 4112 6148 4199 711
         8309 12266 2735 8242 2766 4172 6273 4080 676
         8219 12346 2736 8189 2780 4184 6257 4154 685
         8306 12550 2638 8324 2704 4157 6096 4097 695
         8450 12251 2824 8306 2640 4190 6106 4156 665
         8409 12403 2682 8130 2785 4108 6182 4091 712
         8224 12412 2787 8231 2719 4166 6153 4237 633
         8367 12332 2783 8283 2749 4225 6066 4135 645
          8358 12458 2732 8171 2761 4140 6156 4066 724
          8309 12425 2782 8290 2809 4076 6222 4005 696
          8286 12437 2697 8316 2727 4186 6152 4077 685
          8321 12482 2678 8115 2751 4178 6084 4267 675
           8275 12451 2703 8194 2667 4105 6299 4172 691

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These are all fibered over 4=2 in Gr(2,4) with fiber 6=5 in Gr(2,5).     These all have Galois group S5WrS2, which has order 28800
Schubert Problem (10) (8,2) (6,4) (6,2,2) (5,5) (5,4,1) (5,3,2) (5,3,1,1) (5,2,2,1) (5,2,1,1,1) (5,1,1,1,1,1) (4,4,2) (4,4,1,1) (4,3,2,1) (4,3,1,1,1) (4,2,2,2) (4,2,2,1,1) (4,2,1,1,1,1) (4,1,1,1,1,1,1) (3,3,2,2) (3,3,2,1,1) (3,3,1,1,1,1) (3,2,2,2,1) (3,2,2,1,1,1) (3,2,1,1,1,1,1) (3,1,1,1,1,1,1,1) (2,2,2,2,2) (2,2,2,2,1,1) (2,2,2,1,1,1,1) (2,2,1,1,1,1,1,1) (2,1,1,1,1,1,1,1,1) (1,1,1,1,1,1,1,1,1,1)  
        5103 6058 4135 4139 908 2539 1599 1673 1207 831 78 3035 1528 2067 2072 2116 1536 1030 97 668 1384 677 1065 1747 709 60 214 391 541 233 27 7  
         4976 6209 4226 4061 1018 2383 1636 1641 1321 798 85 3150 1542 2007 2040 2068 1521 1053 103 678 1388 680 1017 1735 752 74 206 371 550 192 28 1  
         4887 6269 4163 4063 971 2488 1634 1673 1286 875 67 3123 1567 2051 2116 1980 1551 1020 115 654 1400 665 1026 1708 804 59 208 350 538 218 33 3  
          5004 6135 4231 4184 951 2373 1620 1655 1252 809 91 3055 1552 2042 2081 2046 1570 1098 103 713 1345 663 1018 1739 757 61 221 362 502 223 40 1  
          5073 6114 4102 4203 960 2428 1636 1698 1283 796 84 3028 1533 2027 2095 2049 1612 1037 113 707 1390 727 1004 1711 715 67 208 400 484 223 45 0  
          5066 6080 4186 4149 987 2496 1577 1606 1232 818 80 3174 1571 2062 2071 2137 1535 992 98 636 1334 678 1062 1763 742 73 221 345 530 213 30 2  
           4913 6278 4133 4242 1014 2466 1624 1598 1236 790 91 3088 1511 2061 2093 2053 1511 1036 110 707 1304 733 1019 1797 763 72 207 362 521 223 32 0  
           4936 6333 4178 4114 993 2478 1647 1683 1241 816 71 3121 1556 2083 2022 1990 1467 1008 108 701 1374 693 1044 1684 771 55 201 391 512 220 46 1  
            5086 6158 4126 4160 983 2440 1672 1684 1300 827 90 3057 1553 1980 2082 2044 1525 1078 81 649 1325 739 1017 1728 790 66 199 419 488 206 35 2  
These have the same Galois group, S2[S2], which has order 8
Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)
      12491 18442 12357 6267
       12503 18562 12329 6177
       12572 18495 12235 6238
        12496 18561 12390 6089
        12563 18476 12376 6151
         12356 18652 12401 6210
         12482 18385 12354 6303
          12385 18567 12368 6289
These have the same Galois group, S2[S2], which has order 8
Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)
      12455 18577 12465 6067
       12438 18580 12374 6175
       12559 18666 12149 6174
        12579 18538 12307 6131
These have the same Galois group, S2[S2], which has order 8
These form one sporadic family
Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)
      12645 18520 12292 6149
       12377 18634 12328 6280
These have the same Galois group, S2[S2], which has order 8
These form another sporadic family
Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)
      12464 18623 12399 6080
       12408 18734 12261 6150
        12563 18661 12196 6109
These have the same Galois group, S2[S2], which has order 8
FiberSchubert Problem (4) (2,2) (2,1,1) (1,1,1,1)
˙˙˙       12480 18649 12223 6206
˙˙˙1˙        12551 18437 12440 6120
˙˙˙       12544 18589 12220 6157
˙˙˙1˙        12688 18542 12240 6047
˙˙˙       12531 18623 12324 6055
˙˙˙1˙        12601 18597 12266 6063
1˙˙˙˙        12473 18555 12182 6344
1˙˙˙1˙˙         12571 18463 12386 6134
1˙˙˙˙        12549 18597 12186 6191
1˙˙˙˙        12255 18731 12373 6225
1˙˙˙1˙˙         12458 18587 12374 6167
These have the same Galois group, S2[S2], which has order 8
FiberSchubert Problem (4) (2,2) (2,1,1) (1,1,1,1)
˙˙˙        12549 18499 12222 6279
˙˙˙1˙         12309 18648 12503 6097
1˙˙˙˙         12405 18663 12391 6129
1˙˙˙1˙˙          12579 18661 12241 6110
This nonreduced problem has Galois group S4
Schubert Problem (4,2) (3,3) (2,2,1,1) (1,1,1,1,1,1)
      12486 16539 18426 2109
These have the same Galois group, S2WrS3, which has order 48.
Schubert Problem (6) (4,2) (4,1,1) (3,3) (2,2,2) (2,2,1,1) (2,1,1,1,1) (1,1,1,1,1,1)
       8245 6251 6309 8215 7184 9215 3162 965
       8329 6246 6075 8370 7217 9116 3089 1048
       8192 6236 6188 8208 7167 9271 3163 1062
        8111 6140 6173 8539 7190 9328 3020 1066
        8268 6133 6295 8286 7149 9151 3149 1021
        8380 6158 6113 8340 7291 9164 3068 1028
        8256 6168 6204 8082 7264 9407 3071 1049
         8300 6323 6180 8212 7259 9258 3074 997
         8219 6241 6183 8331 7201 9327 3071 953
         8467 6076 6177 8296 7194 9273 3058 1041
         8240 6070 6176 8372 7275 9322 3057 1005
          8319 6225 6163 8084 7309 9345 3067 1050
          8240 6238 6265 8346 7181 9167 3089 995
          8256 6269 6266 8283 7116 9150 3129 1052
           8266 6124 6242 8202 7257 9303 3105 1033
These have the same Galois group, S2WrS3, which has order 48.
Schubert Problem (6) (4,2) (4,1,1) (3,3) (2,2,2) (2,2,1,1) (2,1,1,1,1) (1,1,1,1,1,1)
       8200 6219 6186 8445 7101 9317 3059 980
       8259 6196 6185 8207 7153 9290 3220 995
        8309 6304 6033 8385 7366 9201 2929 1008
        8306 6217 6129 8357 7285 9208 2954 1049
         8358 6104 6175 8303 7109 9396 3031 1019
These have the same Galois group, S3WrS2, which has order 72
FiberSchubert Problem (6) (4,2) (3,3) (3,2,1) (3,1,1,1) (2,2,2) (2,2,1,1) (2,1,1,1,1) (1,1,1,1,1,1)
˙˙˙˙        8356 12384 2802 8299 2814 4074 6050 3994 692
˙˙˙1˙˙         8274 12438 2720 8196 2708 4137 6306 4015 677
1˙˙˙˙˙         8236 12482 2815 8249 2746 4138 6202 4045 629
1˙˙˙˙1˙˙          8332 12512 2685 8133 2779 4107 6239 4158 652