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Why are orthogonal Latin Square defined the way they are?

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#combinatorics #latin-square
291
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Is a $4×4$ Latin square possible whose trace-sum is 7 or 9 or 13 or 15?

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#latin-square
239
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Modifying circulant Latin Squares

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#matrices #algorithms #trace #latin-square #circulant-matrices
336
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Graph built from orthogonal Latin squares

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#graph-theory #affine-geometry #latin-square
84
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A question asking to prove an array is not a Latin square

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#combinatorics #discrete-mathematics #latin-square
84
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Matrix Multiplication for Latin Squares

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#matrices #statistics #matrix-equations #latin-square
28
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Grid coordinate multiplicities of orthogonal Latin squares

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#abstract-algebra #combinatorics #modular-arithmetic #latin-square
68
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Prove Per(A)=1 if and only if A is a permutation matrix

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#matrices #permutations #latin-square #permanent
137
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Explain why $4$ cannot be replaced by $5$ in part a)

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#combinatorics #orthogonality #combinatorial-proofs #latin-square
108
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Prove that matrix A so that $a_{ij}$ = (m+1)*(i+j) mod n is a symmetric Latin Square with different elements on its diagonal (m is a freely chosen Z)

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#matrices #latin-square
95
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Minimum (maximum) number of swaps in Latin squares

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#combinatorics #permutations #latin-square
208
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generalization of derangements

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#combinatorics #latin-square #derangements
78
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Do the two order-4 Latin square graphs have the same number of Hamilton cycles?

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#graph-theory #hamiltonian-path #latin-square
50
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For which orders does there exist a Latin square which remains a Latin square after replacing each row by its square (interpreted as permutations)?

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#combinatorics #latin-square
1.2k
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Maximize the sum of the diagonal elements of a Graeco-Latin square

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#discrete-optimization #latin-square

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