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A345679 a(n) is the number of disjoint preference profiles in the stable marriage problem with n men and n women.

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%I A345679 #14 Aug 25 2021 21:41:17
%S A345679 1,12,8784,1031049216
%N A345679 a(n) is the number of disjoint preference profiles in the stable marriage problem with n men and n women.
%C A345679 A disjoint profile is defined as a preference profile where each pair of rankings appears exactly once.
%C A345679 A preference profile corresponds to a digit in a complete n^2 X n^2 Sudoku grid.
%C A345679 A disjoint profile corresponds to a digit in a disjoint-groups Sudoku.
%H A345679 Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, <a href="https://arxiv.org/abs/2108.02654">The Stable Matching Problem and Sudoku</a>, arXiv:2108.02654 [math.HO], 2021.
%e A345679 For n=2, there are 16 preference profiles. Each profile is either a disjoint profile or a joint profile. The number of joint profiles is A344693(2) = 4. Thus, the number of disjoint profiles is 12.
%Y A345679 Cf. A185141, A344693.
%K A345679 nonn,more
%O A345679 1,2
%A A345679 _Tanya Khovanova_ and MIT PRIMES STEP Senior group, Jun 22 2021