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 A308853 a(n) is the minimum absolute value of nonzero determinants of order n Latin squares. 8
 1, 3, 18, 80, 75, 126, 196, 144, 405 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS We apply every symbol permutation on the representatives of isotopic classes to generate Latin squares of order n and calculate the determinants. These results are based upon work supported by the National Science Foundation under the grants numbered DMS-1852378 and DMS-1560019. LINKS Brendan McKay, Latin squares Hugo Pfoertner, Occurrence counts of determinant values for n=1..8, zipped (2019). Eric Weisstein's World of Mathematics, Latin square Wikipedia, Latin square EXAMPLE For n=2, the only Latin squares of order 2 are [[1, 2], [2, 1]] and [[2, 1], [1, 2]].  Therefore, the minimum absolute value of the determinants of order 2 Latin squares is 3. PROG (Sage) # Takes a string and turns it into a square matrix of order n def make_matrix(string, n):     m = []     row = []     for i in range(0, n * n):         if string[i] == '\n':             continue         if string[i] == ' ':             continue         row.append(Integer(string[i]) + 1)         if len(row) == n:             m.append(row)             row = []     return matrix(m) # Reads a file and returns a list of the matrices in the file def fetch_matrices(file_name, n):     matrices = []     with open(file_name) as f:         L = f.readlines()     for i in L:         matrices.append(make_matrix(i, n))     return matrices # Takes a matrix and permutates each symbol in the matrix # with the given permutation def permute_matrix(matrix, permutation, n):     copy = deepcopy(matrix)     for i in range(0, n):         for j in range(0 , n):             copy[i, j] = permutation[copy[i][j] - 1]     return copy """ Creates a determinant list with the following triples, [Isotopy Class Representative, Permutation, Determinant] The Isotopy class representatives come from a file that contains all Isotopy classes. """ def create_determinant_list(file_name, n):     the_list = []     permu = (Permutations(n)).list()     matrices = fetch_matrices(file_name, n)     for i in range(0, len(matrices)):         for j in permu:             copy = permute_matrix(matrices[i], j, n)             the_list.append([i, j, copy.determinant()])             print(len(the_list))     return the_list # Froylan Maldonado, Jun 28 2019 CROSSREFS Cf. A040082, A301371 (upper bound for maximum determinant of Latin squares of order n), A309258, A309984, A309985. Sequence in context: A056319 A056310 A309259 * A309257 A135371 A086346 Adjacent sequences:  A308850 A308851 A308852 * A308854 A308855 A308856 KEYWORD nonn,more,hard AUTHOR EXTENSIONS a(8) from Hugo Pfoertner, Aug 24 2019 a(9) from Hugo Pfoertner, Aug 27 2019 STATUS approved

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Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)