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A344668 a(n) is the number of preference profiles in the stable marriage problem with n men and n women that generate exactly 1 possible stable matching. 3

%I #11 Feb 11 2022 12:13:25

%S 1,14,34080,65867261184

%N a(n) is the number of preference profiles in the stable marriage problem with n men and n women that generate exactly 1 possible stable matching.

%C A069124(n) provides the lower bound for the maximum number of stable matchings with n men and n women. It is exact for n below 5.

%H 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/2201.00645">Sequences of the Stable Matching Problem</a>, arXiv:2201.00645 [math.HO], 2021.

%e For n=2, there are 16 possible preference profiles: 14 of them generate one stable matching and 2 of them generate two stable matchings. Thus, a(2) = 14.

%Y Cf. A069124, A185141, A344666, A344667, A344669.

%K nonn,more

%O 1,2

%A _Tanya Khovanova_ and MIT PRIMES STEP Senior group, May 27 2021

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Last modified June 21 19:01 EDT 2024. Contains 373557 sequences. (Running on oeis4.)