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Knots in Braid notation

Alternating 10-Crossing Knots

The knots page explains the above terms and the notation used in the table.


Number    Conway         b Braid notation
10(1)     21111112       = 5:AbCbdCbaCbCbDC
10(2)     211,21,21      = 5:ABccDcbacDcbcDcB
10(3)     2211112        = 5:AbCbabCbdCbCCD
10(4)     211,21,2+      = 5:ABBcDcBaBcBD
10(5)     221,21,2       = 4:AbbCbacBccBBc
10(6)     .22.2          = 4:ABccbAbbAcBcb
10(7)     22,21,2+       = 5:aBcDcBAcBBdccB
10(8)     .210.2.2       = 4:AAbcBcbbAbbcB
10(9)     (21,2)(21,2)   = 5:aBcdcBBABccDcB
10(10)    210:2:20       = 5:AbCbdCbabCDCCb
10(11)    222112         = 4:AbAAbccBcbb
10(12)    .21.210        = 5:AbCdCBaCdCbCdCBC
10(13)    .21.21         = 5:ABcDcbacBDcDcB
10(14)    212212         = 5:AbbCbabCdCbCCD
10(15)    2332           = 5:aBBccdCbCBAbDCbc
10(16)    321112         = 4:AbAAbcccBcb
10(17)    .31.20         = 4:AbCCbCbaBcBCC
10(18)    32,21,2        = 4:AbCbaccBccBBc
10(19)    3,21,2++       = 4:aaabCbbaCCB
10(20)    33112          = 4:abCbAccccBcBB
10(21)    31132          = 5:abCbAccdCbCBDcBB
10(22)    311113         = 5:ABcBaCCbCbdcBcbD
10(23)    31,3,21        = 4:abCbAccBcccBB
10(24)    4312           = 4:abCbAcBBccccB
10(25)    8*2:20         = 4:AbcBcbABcbAbb
10(26)    8*2:.2         = 3:AAbAbbAbAb
10(27)    2.2.2.2        = 3:AAbbAAbbAb
10(28)    9*20           = 4:ABBcBcBAbABcb
10(29)    8*20.20        = 5:AbCbCDCbabCdCb
10(30)    8*21           = 4:AbccBcbABcbAb
10(31)    .2.2.20.20     = 3:AbbAAbAAbb
10(32)    3:20:20        = 3:aaBaBaaBBB
10(33)    .3.2.20        = 3:AbbAbAAAbb
10(34)    30:2:2         = 4:abCCbCCbACBcB
10(35)    (3,2)(3,2)     = 3:aaaBBaaBBB
10(36)    41,3,2         = 3:aaaBaaBBBB
10(37)    4114           = 3:AbAAAAbbbb
10(38)    10*            = 3:AbAbAbAbAb
10(39)    211,211,2      = 5:aBcDcBABDcBc
10(40)    21,21,21+      = 5:ABcDcbacDcbcDcBD
10(41)    221212         = 5:AbCdCbaCCbCbDC
10(42)    22,211,2       = 5:aBccDcBAcBdcBc
10(43)    2121112        = 5:AbCdCbaCbCbDCC
10(44)    .21.2.20       = 4:AbCbbaaabCb
10(45)    21,21,2++      = 5:abCdCCBACCBCdCbC
10(46)    .22.20         = 4:abCbbAcBcBcBB
10(47)    22,22,2        = 6:ABcDcbacbCCDEDcBcDe
10(48)    22312          = 4:aBaBCCbCBBB
10(49)    23122          = 5:AbCDcDCCbaCbCdCBDc
10(50)    23,21,2        = 5:aBCCCBAcdCBcBDDD
10(51)    24112          = 5:AbCbaCDDcbCdCBDC
10(52)    2422           = 6:abcDcBAdEdCBdCedCbC
10(53)    22,3,2+        = 5:ABcDcbaBcccBDc
10(54)    .31.2          = 4:abbCbCbACBcBC
10(55)    211,3,2+       = 4:abbCbbbAcBcBc
10(56)    31,21,21       = 4:aBCCCCBBABBcB
10(57)    311,21,2       = 5:aBCCCBAdCbCBDBcB
10(58)    311122         = 4:aaaBaBBCCbC
10(59)    (3,2)(21,2)    = 4:aBCCCBABBBcBB
10(60)    312112         = 5:AbCbaCbCdCBDDcDC
10(61)    32212          = 4:aBaBCCCbCBB
10(62)    31222          = 5:AbCdCbabCbDCCC
10(63)    22,3,21        = 5:AbCDcbaDCCCbCdCBDc
10(64)    221,3,2        = 4:AbccBcbAbbb
10(65)    3232           = 5:AbCdCBaDDDcbCCDcBc
10(66)    3412           = 4:AbCbaBcBCCCCC
10(67)    41122          = 5:abcDcBAdCCBBcBdC
10(68)    42112          = 4:aBaBCCCCbCB
10(69)    4,21,21        = 5:aBcdCbCBABDCCCBB
10(70)    41,21,2        = 4:aBCCCCCBBABcB
10(71)    32113          = 4:abCbAcccBcBBB
10(72)    3,3,21+        = 5:ABCCDcbacDcbDCdCBD
10(73)    3,3,2++        = 4:abCbbbAcBcccB
10(74)    4222           = 6:AbCdCBaDEDcbcDcBeDc
10(75)    32,3,2         = 4:abCbAcccBcccB
10(76)    3313           = 4:abCbAcBBBcccB
10(77)    352            = 5:ABCbCdcBaCbCCCbD
10(78)    5212           = 5:ABCbCdcBaCCCbCbD
10(79)    4123           = 5:AbbcBcbDCbaBcBCd
10(80)    433            = 5:aBBBcdCbCBAbDCbc
10(81)    532            = 4:AbCCCCCbaBcBC
10(82)    8*20::20       = 5:aBCDDCCBcdCBABcB
10(83)    21:20:20       = 5:aBcdcBABccDcBc
10(84)    .2.21.2        = 5:AbCbabCdCbCd
10(85)    8*2:.20        = 4:AAbcBcbABcbAb
10(86)    .2.210.2       = 5:ABcdCdcbbaBCdcBc
10(87)    9*.20          = 4:AbcBAbcBAcbAb
10(88)    8*2:2          = 3:AAbAAbAbAb
10(89)    2.2.2.20       = 5:aBBcBDcBABcdcB
10(90)    21:2:2         = 5:AbCbabcdddccbCDc
10(91)    2.2.20.2       = 4:ABcbbbAbbcBcb
10(92)    .2.2.2.20      = 4:AAbABcBBBAbcB
10(93)    8*30           = 4:abCbCbCbACBcB
10(94)    8*3            = 3:AAAbAbAbAb
10(95)    .3.2.2         = 4:AbCbaBcBBccBc
10(96)    30:2:20        = 3:aaaBaBaaBB
10(97)    .30.2.2        = 3:aBBaaBaaaB
10(98)    3:2:20         = 4:AbCbaBcBccBBc
10(99)    .4.2           = 3:AbAbAAAAbb
10(100)   31,3,3         = 3:aaaBaaaBBB
10(101)   5113           = 3:AbAAAbbbbb
10(102)   64             = 6:ABCbCdcBaCbCedcBcbDED
10(103)   23,3,2         = 4:AbbCCbbbaBcBC
10(104)   2512           = 5:aBBccBAbDcBcdCbc
10(105)   31312          = 5:abccdCBACCbcDcBddC
10(106)   4132           = 4:AbCCbbbbaBcBC
10(107)   41113          = 4:abCbAcBBBBcBc
10(108)   51112          = 5:aBcBBAbDcBcdCbcc
10(109)   311,3,2        = 4:AbbbCbbaBcBCC
10(110)   30:20:20       = 4:AbbCbCbbaBcBC
10(111)   .3.20.2        = 4:abCbAcBcBBcBB
10(112)   3:2:2          = 3:AAAbAAbAAb
10(113)   .4.20          = 3:AAAAbAAbAb
10(114)   211,3,3        = 5:ABccDcbaCCDcbCdCBD
10(115)   4,3,21         = 3:AAbbbbAbbb
10(116)   5,21,2         = 3:aaaaaBaaBB
10(117)   6112           = 3:AbAAbbbbbb
10(118)   4,3,3          = 4:AbbbCbbbaBcBC
10(119)   712            = 3:aBaBBBBBBB
10(120)   82             = 6:AbCdCBaDEdCbDcDcBCeDc
10(121)   514            = 4:abCbAcBcBBBBB
10(122)   613            = 5:aBBBcBAbDcBcdCbc
10(123)   5,3,2          = 3:AbbbbbAbbb

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