Two edges, two corners transpositions

These sequences are transpositions of two corners and two edges. The shortest algorithm for a transposition of two edges and two corners has 13 quarter moves. The list below is an attempt to find all 13 and 15 quarter-move algorithms. The list was found by hands and is by no means considered to be complete. If you would like to add some new algorithms, please contact Mirek Goljan mgoljan (AT) binghamton. edu Jessica.

The two groups of the same length are sorted in alphabetical order. The alphabet is: A²s,A²,As,Aa,A,A'a,A',B²s,B²,Bs,Ba,B, B'a,B', ... ,F²s,F²,Fs,Fa,F,F'a,F'. Faces A,B,C,D,E,F represent U,R,D,L,B,F respectively in English notation and if you want you can easily transfer algorithms to this or any other notation. Every algorithm is put in its minimal form (in alphabetical order) of all its cyclic shifts, inversions, mirrorings, and whole cube rotations. Number of a sequence means a number of quarter moves, [number] means number of used faces.

                               moves  faces  name
A²B²C E C'B²A F'A F             (13)  [5]   CE1351
A²BaA'B'A D'A²B A'B'            (13)  [3]   CE1331
A²B A B²C'F C B F'A F           (13)  [4]   CE1341
A²B A B'A D F D'A'F'A F         (13)  [4]   CE1342
A²B A B'A E'A B A B'A'E         (13)  [3]   CE1332
A²B A B'A E'B E A E'B'E         (13)  [3]   CE1336
A²B A B'A F'A E D E'A'F         (13)  [5]   CE1352
A²B A B'A F'A'B'F B A F         (13)  [3]   CE1333
A²B A B'A F'D C F C'D'F         (13)  [5]   CE1353
A²B A F'A E D'A'D F A E'        (13)  [5]   CE1357
A²B A'B'A'E B E'A'E B'E'        (13)  [3]   CE1334
A²B A'B'A'E D A'F'A D'E'        (13)  [5]   CE1355
AaB'A'B C'B A F B'F'A'B'        (13)  [4]   CE1344
A B A B'A D F A'F'A F A D'      (13)  [4]   CE1343
A B A B'A F'A E D A'F A E'      (13)  [5]   CE1354
A B A B'A'E'A'E B E'A E B'      (13)  [3]   CE1335
A B A B'A'E'A'E D A'F A D'      (13)  [5]   CE1356
			        moves  faces  name
A²BsA E A'E'B'A D A D'A D       (15)  [4]   CE1501
A²BaA B²D'C'D F²D'C B           (15)  [5]   CE1502
A²B A²B'F'B'F B F'D F D'F       (15)  [4]   CE1503
A²B A²E A E'B'E'F'A F A'E       (15)  [4]   CE1504
A²B A²E D'E D E²B'E'B E         (15)  [4]   CE1505
A²B A B²A D A'B A B D'A B'      (15)  [3]   CE1506
A²B A B²A'E'B E B A F'A F       (15)  [4]   CE1507
A²B A B A'B'A F A'B'A B A F'    (15)  [3]   CE1508
A²B A B F B F'A'B²A F'A F       (15)  [3]   CE1509
A²B A B'A B A E'B'F'B E B'F     (15)  [4]   CE1510
A²B A B'A B F'A E A'F A E'B'    (15)  [4]   CE1511
A²B A B'A B F'D'A'D A F A B'    (15)  [4]   CE1512
A²B A B'A E'B E A D'E'B'E D     (15)  [4]   CE1513
A²B A B'A F'A D E D E'A'D'F     (15)  [5]   CE1514
A²B A B'A F'A D'A'D F D F D'    (15)  [4]   CE1515
A²B A B'A F'A D'A'F'D F D F'    (15)  [4]   CE1516
A²B A B'A F'D F²D'A'F A F'      (15)  [4]   CE1517
A²B A B'A F'D F B F'D'F A B'    (15)  [4]   CE1518
A²B A B'A F'D F D C'D'C F D'    (15)  [5]   CE1519
A²B A B'A F'D F D'F A D'A'D     (15)  [4]   CE1520
A²B A B'D'A B A'D A E A E'B'    (15)  [4]   CE1521
A²B A B'D'E D F'D'E'A D A F     (15)  [5]   CE1522
A²B A B'E F'A'D'A D A E'A F     (15)  [5]   CE1523
A²B A B'E F'A'F A E'A B A B'    (15)  [4]   CE1524
A²B A B'E F'D'E'A E D E'A F     (15)  [5]   CE1525
A²B A B'F'B'F B A F'D F D'F     (15)  [4]   CE1526
A²B A B'F'D'A D A E'A F A'E     (15)  [5]   CE1527
A²B A D'A E A²B'A'E'A'E D       (15)  [4]   CE1528
A²B A E A'B'A E'A E D'E D E'    (15)  [4]   CE1529
A²B A F B F'B'F'A F'D F D'F     (15)  [4]   CE1530
A²B A'B'A'B A'E D E'B'E D'E'    (15)  [4]   CE1531
A²B A'B'A'B E'C'E A'E'C E B'    (15)  [4]   CE1532
A²B A'B'A'D A'F'D F'D'F A D'    (15)  [4]   CE1533
A²B A'B'A'D A'F'D'A E D'E'D     (15)  [5]   CE1534
A²B A'D A B'A F A B A B'F'D'    (15)  [4]   CE1535
A²B A'E'B C'B'E A'B'F'B'F B     (15)  [5]   CE1536
A²B A'F'A B'A'F A'B'F'B'F B     (15)  [3]   CE1537
A²B A'F'A B'A'F A'F B F'B'F'    (15)  [3]   CE1538
A²B E A E'B'A F'A F B'F B F'    (15)  [4]   CE1539
A²B E B E'B'A B'A F B'C B F'    (15)  [5]   CE1540
A²B E D A'D'A'E'A'B E'B'E B'    (15)  [4]   CE1541
AsB A'B'AaB'A'B E'C'B'C E       (15)  [4]   CE1542
AsB C B'A'E'B E C'B'C E'B'E     (15)  [4]   CE1543
A B A B'A D C'F A'F'A C F A D'  (15)  [5]   CE1544
A B A B'A E'A B A B'F A'E A F'  (15)  [4]   CE1545
A B A'E D'A D E'A B'F B A'B'F'  (15)  [5]   CE1546

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