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Connected Fair Detachments of Hypergraphs II
Amin Bahmanian
We study embeddings of factorizations of the -fold complete -uniform hypergraph in factorizations of , where and both the source and target degrees may…
A Hadamard Cube of Order 22
Amin Bahmanian, Sho Suda
We give an explicit three-dimensional Hadamard matrix of order . The example is presented by listing its twenty-two two-dimensional slices.
Sudoku Analogues of Baranyai's Theorem
Amin Bahmanian, Sho Suda
Motivated by higher-dimensional generalizations of Sudoku, we study exact block-structured decompositions, algebraic characterizations, and orthogonality for Sudoku hypercubes. Let…
Extending Symmetric Layer-Rainbow Latin Cubes
Amin Bahmanian
An array on symbols is a layer-rainbow Latin cube if every layer contains every symbol exactly once. We call it symmetric if $L_{ij\ell}=L_{j\ell i}=L_{\e…
The Andersen-Hoffman Theorem for Equitable Rectangles
Amin Bahmanian, Anna Johnsen-Yu
More than forty years ago, Andersen and Hoffman independently proved that every symmetric Latin rectangle can be extended to a symmetric Latin square with prescribed diagonal entri…
Embedding Equitable Rectangles
Amin Bahmanian, Anna Johnsen-Yu
Completing partial Latin squares is NP-complete. Ryser characterized precisely when an Latin rectangle can be completed to an Latin square. We extend this t…
Hadamard Hypercubes
Amin Bahmanian, Sho Suda
Although Hadamard matrices have been investigated since the nineteenth century, relatively little is known about their higher-dimensional analogues. In this paper, we introduce two…