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Number of regular elements in the semigroup of all binary relations on [n].

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`%I #11 Jun 17 2022 15:55:46
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`%S 1,2,16,470,40408,8683982
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`%N Number of regular elements in the semigroup of all binary relations on [n].
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`%C Let S be a semigroup. An element A in S is regular iff A = A*B*A for some B in S. An element in the semigroup of all binary relations is regular iff its row space forms a distributive lattice under set inclusion.
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`%H K. K.-H. Butler and G. Markowsky, <a href="https://www.koreascience.or.kr/article/JAKO197225748110925.pdf">The Number of Maximal Subgroups of the Semigroup of Binary Relations</a>, Kyungpook Math. J. Vol 12, June 1972.
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`%Y Cf. A003425.
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`%K nonn,more
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`%O 0,2
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`%A _Geoffrey Critzer_, May 22 2022
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