Thomas Zasĺavsky

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math.CO2010

Perpendicular dissections of space

Thomas Zaslavsky

For each pair $(Q_{i}, Q_{j})$ of reference points and each real number $r$ there is a unique hyperplane $h ⊥ Q_{i} Q_{j}$ such that $d (P, Q_{i})^{2} - d (P, Q_{j})^{2} = r$ for points $P$ in $h$ .…

math.CO2010

An elementary chromatic reduction for gain graphs and special hyperplane arrangements

Pascal Berthome, Raul Cordovil, David Forge +2

A gain graph is a graph whose edges are labelled invertibly by "gains" from a group. "Switching" is a transformation of gain graphs that generalizes conjugation in a group. A "weak…