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Opis: We study n-dimensional matrices with {0, 1}-entries (n-cubes) such that all their 2-dimensional slices are incidence matrices of symmetric designs. A known construction of these objects obtained from difference sets is generalized so that the resulting n-cubes may have inequivalent slices. For suitable parameters, they can be transformed into n-dimensional Hadamard matrices with this property. In contrast, previously known constructions of n-dimensional designs all give examples with equivalent slices.
Ključne besede: symmetric design, difference set, Hadamard matrix
Objavljeno v RUP: 21.10.2025; Ogledov: 255; Prenosov: 0
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Opis: It is shown that the graph ▫$\Gamma_n$▫ that has the set of all ▫$n \times n$▫ symmetric matrices over a finite field as the vertex set, with two matrices being adjacent if and only if the rank of their difference equals one, is a core if ▫$n \ge 3$▫. Eigenvalues of the graph ▫$\Gamma_n$▫ are calculated as well.
Ključne besede: adjacency preserver, symmetric matrix, finite field, eigenvalue of a graph, coloring, quadratic form
Objavljeno v RUP: 15.10.2013; Ogledov: 5438; Prenosov: 149
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