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.

1, 14, 34080, 65867261184

Offset: 1

Author

Tanya Khovanova and MIT PRIMES STEP Senior group, May 27 2021

Keywords

• nonn
• more

Comments

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.

Examples

			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.
		

Links

• Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, Sequences of the Stable Matching Problem, arXiv:2201.00645 [math.HO], 2021.

Crossrefs

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