A344667 a(n) is the number of preference profiles in the stable marriage problem with 4 men and 4 women that generate n possible stable matchings.

65867261184, 35927285472, 7303612896, 861578352, 111479616, 3478608, 581472, 36432, 0, 144

Offset: 1

Author

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

Keywords

• nonn
• fini
• full

Comments

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

A185141(4) = 110075314176 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 3 men and 3 women, the total number of preference profiles is 46656, where the number of possible stable matchings ranges from 1 to 3. The distribution is provided by sequence A344666(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, A344666, A344668, A344669.