The lists below are presented in TeX display math mode so that they may be copied directly into a TeX document. Each list item is numbered as a birack, biquandle, rack or quandle the prefix BR, BQ, R or Q respectively together with the number of crossings as a superscript and an index as a subscript. The up and down actions contained in the lists on this page correspond to the maps f^a and f_a.

• Sideways maps for 3 biracks of size 2 (includes quandles, biquandles and racks)
• Sideways maps for 2 biquandle of size 2 (includes quandles)
• Sideways maps for 2 racks of size 2 (includes quandles)
• Sideways maps for 1 quandle of size 2
• There are no biracks of size 2 that are not biquandles and not racks
• Sideways maps for 1 biquandle of size 2 that is not a quandle
• Sideways maps for 1 rack of size 2 that is not a quandle
• Sideways maps for 2 quandle-related biracks of size 2
• Sideways maps for 1 quandle-related birack of size 2 that is not a quandle
• There are no quandle-related biquandles of size 2 that are not quandles


• Sideways maps for 16 biracks of size 3 (includes quandles, biquandles and racks)
• Sideways maps for 10 biquandles of size 3 (includes quandles)
• Sideways maps for 6 racks of size 3 (includes quandles)
• Sideways maps for 3 quandles of size 3
• Sideways maps for 3 biracks of size 3 that are not biquandles and not racks
• Sideways maps for 7 biquandles of size 3 that are not quandles
• Sideways maps for 3 racks of size 3 that are not quandles
• Sideways maps for 9 quandle-related biracks of size 3
• Sideways maps for 6 quandle-related biracks of size 3 that are not quandles
• Sideways maps for 1 quandle-related biquandle of size 3 that is not a quandle


• Sideways maps for 147 biracks of size 4 (includes quandles, biquandles and racks)
• Sideways maps for 64 biquandle of size 4 (includes quandles)
• Sideways maps for 19 racks of size 4 (includes quandles)
• Sideways maps for 7 quandles of size 4
• Sideways maps for 71 biracks of size 4 that are not biquandles and not racks
• Sideways maps for 57 biquandles of size 4 that are not quandles
• Sideways maps for 12 racks of size 4 that are not quandles
• Sideways maps for 60 quandle-related biracks of size 4
• Sideways maps for 53 quandle-related biracks of size 4 that are not quandles
• Sideways maps for 11 quandle-related biquandles of size 4 that are not quandles


• Sideways maps for 703 quandle-related biracks of size 5 (includes quandles, biquandles and racks)
• Sideways maps for 134 quandle-related biquandles of size 5 (includes quandles)
• Sideways maps for 73 racks of size 5 (includes quandles)
• Sideways maps for 21 quandles of size 5
• Sideways maps for 517 quandle-related biracks of size 5 that are not biquandles and not racks
• Sideways maps for 682 quandle-related biracks of size 5 that are not quandles (includes biquandles and racks)
• Sideways maps for 113 quandle-related biquandles of size 5 that are not quandles
• Sideways maps for 52 racks of size 5 that are not quandles


• Sideways maps for 13562 quandle-related biracks of size 6 (includes quandles, biquandles and racks)
• Sideways maps for 1578 quandle-related biquandles of size 6 (includes quandles)
• Sideways maps for 352 racks of size 6 (includes quandles)
• Sideways maps for 72 quandles of size 6
• Sideways maps for 11704 quandle-related biracks of size 6 that are not biquandles and not racks
• Sideways maps for 13490 quandle-related biracks of size 6 that are not quandles (includes biquandles and racks)
• Sideways maps for 1506 quandle-related biquandles of size 6 that are not quandles
• Sideways maps for 280 racks of size 6 that are not quandles

The above lists were calculated from the plain switch lists using the script convert-maps with the commands convert-maps -n <n> -o T, where <n> took values 2,...,6 and -o T identifies TeX format.

back to finite biquandles back to maths homepage