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

1, 12, 8784, 1031049216

Offset: 1

Author

Tanya Khovanova and MIT PRIMES STEP Senior group, Jun 22 2021

Keywords

• nonn
• more

Comments

A disjoint profile is defined as a preference profile where each pair of rankings appears exactly once.

A preference profile corresponds to a digit in a complete n^2 X n^2 Sudoku grid.

A disjoint profile corresponds to a digit in a disjoint-groups Sudoku.

Examples

			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.
		

Links

• Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, The Stable Matching Problem and Sudoku, arXiv:2108.02654 [math.HO], 2021.

Crossrefs

Cf. A185141, A344693.