cp's OEIS Frontend

A069124 Number of stable matchings in a certain form of Pseudo-Latin squares of order n based on Latin subsquares.

%I A069124 #38 May 17 2025 15:53:53
%S A069124 1,2,3,10,12,32,42,268,288,656,924,4360,3816,11336,13536,195472,
%T A069124 200832,423104,618576,2404960,2506464,6994784,8820864,85524160,
%U A069124 60669696,145981952,194348448,1073479840
%N A069124 Number of stable matchings in a certain form of Pseudo-Latin squares of order n based on Latin subsquares.
%C A069124 a(n) is from Table 1 of Thurber's linked paper. The particular form of Pseudo-Latin squares is based on upper-left subsquares of the power-of-2 Latin squares of A005154, defined as G(n) in Section 3 of Thurber's paper. - _Dan Eilers_, May 16 2025
%C A069124 There is a possibility that some of the terms in this sequence from a(7) onward are incorrect. See A371810 for an alternative. - _Sean A. Irvine_, Apr 16 2024
%C A069124 a(7)=42 verified using MiniZinc, see linked file with details. - _Dan Eilers_, May 14 2025
%H A069124 Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, <a href="https://arxiv.org/abs/2108.02654">The Stable Matching Problem and Sudoku</a>, arXiv:2108.02654 [math.HO], 2021.
%H A069124 Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, <a href="https://arxiv.org/abs/2201.00645">Sequences of the Stable Matching Problem</a>, arXiv:2201.00645 [math.HO], 2021.
%H A069124 Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, <a href="https://doi.org/10.1080/07468342.2023.2261183">The Stable Marriage Problem and Sudoku</a>, College Math. J. (2023).
%H A069124 Dan Eilers, <a href="/A069124/a069124.txt">Response to Sean A. Irvine comment regarding a(7)=42</a>, 2025.
%H A069124 Peter J. Stuckey, Kim Marriott, and Guido Tack, <a href="https://docs.minizinc.dev/en/stable/modelling2.html#array-access-constraints">The MiniZinc Handbook, Listing 2.2.12, stable-marriage.mzn</a>, Version 2.9.2, 6 March 2025.
%H A069124 E. G. Thurber, <a href="https://doi.org/10.1016/S0012-365X(01)00194-7">Concerning the maximum number of stable matchings in the stable marriage problem</a>, Discrete Math., 248 (2002), 195-219.
%Y A069124 Cf. A371810.
%Y A069124 Cf. A005154 (power-of-2 Latin squares used as basis for subsquares). - _Dan Eilers_, May 16 2025
%K A069124 nonn,more
%O A069124 1,2
%A A069124 _N. J. A. Sloane_, Apr 12 2002
%E A069124 Name edited by _Dan Eilers_, May 16 2025