A344666 a(n) is the number of preference profiles in the stable marriage problem with 3 men and 3 women that generate n possible stable matchings.

34080, 11484, 1092

Offset: 1

Author

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

Keywords

• nonn
• bref
• fini
• full

Comments

A185141(n) is the total number of preference profiles for n men and n women.

A185141(3) = 46656 is the sum of the terms of this sequence.

For 2 men and 2 women, the total number of preference profiles is 16, where 14 profiles have 1 stable matching, and 2 profiles have 2 stable matchings.

For 4 men and 4 women, the total number of preference profiles is 110075314176, where the number of possible stable matchings ranges from 1 to 10, excluding 9. The distribution is provided by sequence A344667(n).

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. A185141, A344667, A344668, A344669.