The lists below are presented in a plain text format as two matrices one for the up action (U) and one for the down action (D). Each matrix is specified row by row. 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>, where <n> took values 2,...,6.

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