On geometric trilateral-free (n_3) configurations

Raney, Michael

doi:10.26493/1855-3974.273.c0f

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…For example, Trenkler [47] studied magic stars which are configurations with two lines through every point. More recently, Raney [35] studied magic trilateral free n 3 -configurations where three lines pass through every point, and each line contains three points. In addition, Nash and Needleman [33] studied magic finite projective planes which are configurations which contain a quadrilateral and further require all lines to intersect, and all pairs of points to be connected by a line.…”

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confidence: 99%

Non-magic Hypergraphs

Ellis,

Nash,

Needleman

et al. 2018

Preprint

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This article studies a generalization of magic squares to k-uniform hypergraphs. In traditional magic squares the entries come from the natural numbers. A magic labeling of the vertices in a graph or hypergraph has since been generalized to allow for labels coming from any abelian group. We demonstrate an algorithm for determining whether a given hypergraph has a magic labeling over some abelian group. A slight adjustment of this algorithm also allows one to determine whether a given hypergraph can be magically labeled over Z. As a demonstration, we use these algorithms to determine the number of magic n3-configurations for n = 7, . . . , 14.

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confidence: 99%

Non-magic Hypergraphs

Ellis,

Nash,

Needleman

et al. 2018

Preprint

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“…These are designs where every line has the same number of points, and every point has the same number of lines through it. Magic stars are an example with two lines through every point [8] and more recently Raney studied magic configurations where three lines pass through every point, and each line contains three points [7].…”

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confidence: 99%

When Are Finite Projective Planes Magic?

Nash

Needleman

2016

Mathematics Magazine

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This article studies a generalization of magic squares to finite projective planes. In traditional magic squares the entries come from the natural numbers. This does not work for finite projective planes, so we instead use Abelian groups. For each finite projective plane we demonstrate a small group over which the plane can labeled magically. In the prime order case we classify all groups over which the projective plane can be made magic.

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