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Automorphisms of the Cube \(n^d\)

  • Pavel DvořákEmail author
  • Tomáš Valla
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)

Abstract

Consider a hypergraph \(H_n^d\) where the vertices are points of the d-dimensional combinatorial cube \(n^d\) and the edges are all sets of n points such that they are in one line. We study the structure of the group of automorphisms of \(H_n^d\), i.e., permutations of points of \(n^d\) preserving the edges. In this paper we provide a complete characterization. Moreover, we consider the Colored Cube Isomorphism problem of deciding whether for two colorings of the vertices of \(H_n^d\) there exists an automorphism of \(H_n^d\) preserving the colors. We show that this problem is \(\mathsf {GI}\)-complete.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic
  2. 2.Faculty of Information TechnologyCzech Technical University in PraguePragueCzech Republic

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