This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A301371 #43 Aug 04 2025 04:19:38 %S A301371 1,1,3,18,160,2325,41895,961772,27296640,933251220 %N A301371 Maximum determinant of an n X n matrix with n copies of the numbers 1 .. n. %C A301371 929587995 <= a(9) <= 934173632 (upper bound from Gasper's determinant theorem). The lower bound corresponds to a Latin square provided in A309985, but it is unknown whether a larger determinant value can be achieved by an unconstrained arrangement of the matrix entries. - _Hugo Pfoertner_, Aug 27 2019 %C A301371 Oleg Vlasii found a 9 X 9 matrix significantly exceeding the determinant value achievable by a Latin square. See example and links. - _Hugo Pfoertner_, Nov 04 2020 %H A301371 Ortwin Gasper, Hugo Pfoertner and Markus Sigg, <a href="http://www.emis.de/journals/JIPAM/article1119.html">An Upper Bound for the Determinant of a Matrix with given Entry Sum and Square Sum</a>, JIPAM, Journal of Inequalities in Pure and Applied Mathematics, Volume 10, Issue 3, Article 63, 2008. %H A301371 IBM Research, <a href="https://www.research.ibm.com/haifa/ponderthis/challenges/November2019.html">Large 9x9 determinant</a>, Ponder This Challenge November 2019. %H A301371 Markus Sigg, <a href="https://arxiv.org/abs/1804.02897">Gasper's determinant theorem, revisited</a>, arXiv:1804.02897 [math.CO], 2018. %H A301371 Oleg Vlasii, <a href="https://github.com/OlegV567/Determinant-OEIS-A301371-9">Determinant-OEIS-A301371-9</a>, program and description, 4 Dec 2019. %H A301371 <a href="/index/De#determinants">Index entries for sequences related to maximal determinants</a> %F A301371 A328030(n) <= a(n) <= A328031(n). - _Hugo Pfoertner_, Nov 04 2019 %e A301371 Matrices with maximum determinants: %e A301371 a(2) = 3: %e A301371 (2 1) %e A301371 (1 2) %e A301371 a(3) = 18: %e A301371 (3 1 2) %e A301371 (2 3 1) %e A301371 (1 2 3) %e A301371 a(4) = 160: %e A301371 (4 3 2 1) %e A301371 (1 4 3 2) %e A301371 (3 1 4 3) %e A301371 (2 2 1 4) %e A301371 a(5) = 2325: %e A301371 (5 3 1 2 4) %e A301371 (2 5 4 1 3) %e A301371 (4 1 5 3 2) %e A301371 (3 4 2 5 1) %e A301371 (1 2 3 4 5) %e A301371 a(6) = 41895: %e A301371 (6 1 4 2 3 5) %e A301371 (3 6 2 1 5 4) %e A301371 (4 5 6 3 2 1) %e A301371 (5 3 1 6 4 2) %e A301371 (1 2 5 4 6 3) %e A301371 (2 4 3 5 1 6) %e A301371 a(7) = 961772: %e A301371 (7 2 3 5 1 4 6) %e A301371 (3 7 6 4 2 1 5) %e A301371 (2 1 7 6 4 5 3) %e A301371 (4 5 1 7 6 3 2) %e A301371 (6 3 5 1 7 2 4) %e A301371 (5 6 4 2 3 7 1) %e A301371 (1 4 2 3 5 6 7) %e A301371 a(8) = 27296640: %e A301371 (8 8 3 5 4 3 4 1) %e A301371 (1 8 6 3 1 6 6 5) %e A301371 (5 3 8 1 7 6 4 2) %e A301371 (5 1 6 8 2 4 7 3) %e A301371 (1 5 2 7 8 6 4 3) %e A301371 (7 3 2 4 3 8 2 7) %e A301371 (5 4 2 2 6 2 8 7) %e A301371 (4 5 7 6 5 1 1 7) %e A301371 a(n) is an upper bound for the determinant of an n X n Latin square. a(n) = A309985(n) for n <= 7. a(8) > A309985(8). - _Hugo Pfoertner_, Aug 26 2019 %e A301371 From _Hugo Pfoertner_, Nov 04 2020: (Start) %e A301371 a(9) = 933251220, achieved by a Non-Latin square: %e A301371 (9 5 5 3 3 2 2 8 8) %e A301371 (4 9 2 6 7 5 3 1 8) %e A301371 (4 7 9 2 1 8 6 3 5) %e A301371 (6 3 7 9 4 1 8 2 5) %e A301371 (6 2 8 5 9 7 1 4 3) %e A301371 (7 4 1 8 2 9 5 6 3) %e A301371 (7 6 3 1 8 4 9 5 2) %e A301371 (1 8 6 7 5 3 4 9 2) %e A301371 (1 1 4 4 6 6 7 7 9) %e A301371 found by Oleg Vlasii as an answer to the IBM Ponder This Challenge November 2019. See links. (End) %Y A301371 Cf. A085000, A309985, A328030, A328031. %K A301371 nonn,hard,more %O A301371 0,3 %A A301371 _Hugo Pfoertner_, Mar 21 2018 %E A301371 a(8) from _Hugo Pfoertner_, Aug 26 2019 %E A301371 a(9) from _Hugo Pfoertner_, Nov 04 2020