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

1,2

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.

Links

Table of n, a(n) for n=1..4.

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.

Example

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.

Crossrefs

Cf. A185141, A344693.

Sequence in context: A013513 A013480 A107254 * A012532 A343699 A346717

Adjacent sequences: A345676 A345677 A345678 * A345680 A345681 A345682

Keyword

nonn,more

Author

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

Status

approved