Chad Giusti

Post-Doctoral Research Associate
Mathematical Neuroscience Lab
University of Nebraska -- Lincoln

229 Avery Hall
University of Nebraska -- Lincoln
Lincoln, Nebraska 68588


cgiusti2 "at" standard university e-mail suffix

Plumbers' Knot Gallery

Depicted here are representatives for the components of the spaces of 5 and 6 move plumbers' knots. The components were enumerated using this java code and the images were created using this Mathematica notebook. To classify them, the Jones polynomial for each knot was computed using this Mathematica notebook and the Knot Theory' package.

Representatives for components of K5

00 [1234x1234x1234]
31 (right handed)
[1342x2413x2413] [1342x2413x3124] [2431x2413x4213]
31 (left handed)
[1342x3142x2413] [1342x3142x3124] [2431x3142x4213]

Representatives for components of K6

00 [12345x12345x12345]
31 (right handed)
[24135x31245x23145] [42351x42351x24135] [13524x15324x51342]
31 (left handed)
[12453x13524x13524] [42351x51342x24135] [13524x42351x51342]
[14352x31452x42135] [24153x25314x24315] [31452x31524x32451]
51 (right handed)
[24153x31524x42315] [25134x41253x35241] [15342x24153x42153]
[31542x31524x42315] [41523x41352x34152]
51 (left handed)
[15342x31542x31524] [52413x24513x25314] [15342x31542x42513]
[31542x42315x42315] [41523x25314x34152]
52 (right handed)
[15342x24513x35124] [25413x35124x25314] [25134x24153x35241]
[25413x31524x42315] [15342x24513x42153] [31542x31524x42351]
[15342x25413x31524] [24153x35214x42315] [15342x25413x42513]
[35142x35214x42315] [15342x24153x41253] [31452x31524x42315]
[41523x25314x43152] [41532x41352x34152]
52 (left handed)
[15342x31542x35124] [24513x42153x42315] [25134x35124x35241]
[52413x24513x23514] [15342x31542x42153] [31542x42153x42315]
[15342x31452x31524] [24153x41253x42315] [15342x31452x42513]
[35142x41253x42315] [15342x35142x41253] [31452x42513x42315]
[41523x41352x43152] [41532x25314x34152]