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Is there a procedure to construct all semigroups over a given set without backtracking?

(Edit: see also how many associative binary operations are there on a finite set and ratio of semigroups over a set N to magmas over N goes to 0 as the cardinality of N gets bigger.)

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    We still don't know how many semigroups of order 10 there are I believe. I think $9$ was cracked a couple of years ago.2012-04-30

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