Plans related to the search for (certain) groupoids.
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Detailed Description
Plans related to the search for (certain) groupoids.
 Todo:
 Encodings

For a natural number n, the groupoid structures on {1,...,n} are captured by the n^2 variables c_{i,j}, i,j in {1,...,n} with valuedomains {1,...,n} (the value of c_{i,j} is the composition of i and j). The two most basic constraints are:

Commutativity: c_{i,j} = c_{j,i} (for i <> j). Are there interesting active clausesets? Seems to be completely straightforward, and only a question of appropriate data structures.

Associativity: Much less straightforward, and activeclausesets could be very interesting.
 Todo:
 Quasigroups
 Todo:
 Literature surview

We need overview on the literature.

Searching for interesting problems.

Searching for interesting algorithms.
 Todo:
 Discrete groupoids

I (OK) call a groupoid discrete if x * y in {x,y} is always the case (are there notions for that in the literature?). Discrete groupoids are idempotent, and can be represented by n^2  n many boolean variables (for each pair (i,j) with (i,j) the variables states whether the composition is i or j).

Are there interesting problems?

For a start, one could just search for noncommutative discrete semigroups (while the commutative discrete semigroups correspond 11 to the linear orders on the ground set  composition is min (or max)).

Stronger would be to count all discrete semigroups (on {1,...,n}). For that we need the active clauseset for associativity from above to work with these special variables.
Definition in file Groupoids.hpp.