Dimension 0
trivial
{{0 1 2}}
Dimension 1
reversible & reversible
{{} {0 1 2}}
constant & reversible
{{0 1 2} {2}}
{{0 1 2} {1}}
{{0 1 2} {0}}
constant & constant
{{0 1 2} {1 2}}
{{0 1} {0 1 2}}
{{0 1 2} {0 2}}
constant & function
{{0 1 2} {2} {1 2}}
{{0 1} {0 1 2} {0}}
{{0 1 2} {2} {0 2}}
{{0 1 2} {0 2} {0}}
{{0 1 2} {1} {1 2}}
{{0 1} {0 1 2} {1}}
reversible binary operation which is partially invariant
{{} {0 1 2} {1}}
{{} {0 1 2} {2}}
{{} {0 1 2} {0}}
product to a reversible pair
{{} {0 1 2} {1 2}}
{{} {0 1 2} {0 2}}
{{0 1} {} {0 1 2}}
product to a functional pair
{{} {0 1 2} {2} {1 2}}
{{} {0 1 2} {0 2} {0}}
{{} {0 1 2} {2} {0 2}}
{{} {0 1 2} {1} {1 2}}
{{0 1} {} {0 1 2} {1}}
{{0 1} {} {0 1 2} {0}}
reversible binary operation
{{} {0 1 2} {1} {0}}
{{} {0 1 2} {2} {0}}
{{} {0 1 2} {2} {1}}
any product function
{{} {0 1 2} {2} {0 2} {0}}
{{0 1} {} {0 1 2} {1} {0}}
{{} {0 1 2} {2} {1} {1 2}}
Dimension 2
constant binary operation (disconnected)
{{0 1} {0 1 2} {1} {1 2}}
{{0 1 2} {2} {1 2} {0 2}}
{{0 1} {0 1 2} {0 2} {0}}
1 goes to 2 and 2 goes to 1 (disconnected)
{{} {0 1 2} {1 2} {0}}
{{} {0 1 2} {1} {0 2}}
{{0 1} {} {0 1 2} {2}}
partially invariant operation
{{} {0 1 2} {2} {1} {1 2} {0 2}}
{{} {0 1 2} {2} {1 2} {0 2} {0}}
{{0 1} {} {0 1 2} {1} {1 2} {0}}
{{0 1} {} {0 1 2} {2} {0 2} {0}}
{{0 1} {} {0 1 2} {1} {0 2} {0}}
{{0 1} {} {0 1 2} {2} {1} {1 2}}
partially reversible binary operation
{{0 1} {} {0 1 2} {2} {1}}
{{0 1} {} {0 1 2} {2} {0}}
{{} {0 1 2} {1} {0 2} {0}}
{{} {0 1 2} {2} {1 2} {0}}
{{} {0 1 2} {1} {1 2} {0}}
{{} {0 1 2} {2} {1} {0 2}}
both 1 and 2 go to 0
{{} {0 1 2} {2} {1 2} {0 2}}
{{0 1} {} {0 1 2} {1} {1 2}}
{{0 1} {} {0 1 2} {0 2} {0}}
completely cancellative binary operaiton
{{} {0 1 2} {2} {1} {0}}
partially cancellative binary operation
{{0 1} {} {0 1 2} {2} {1} {0}}
{{} {0 1 2} {2} {1} {1 2} {0}}
{{} {0 1 2} {2} {1} {0 2} {0}}
any binary operations
{{0 1} {} {0 1 2} {2} {1} {1 2} {0}}
{{} {0 1 2} {2} {1} {1 2} {0 2} {0}}
{{0 1} {} {0 1 2} {2} {1} {0 2} {0}}
Dimension 3
any ternary relation (disconnected)
{{0 1} {} {0 1 2} {2} {1} {1 2} {0 2} {0}}
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