Associativity in multiary quasigroups: the way of biased expansions

@article{Zaslavsky2004AssociativityIM,
  title={Associativity in multiary quasigroups: the way of biased expansions},
  author={Thomas Zaslavsky},
  journal={Aequationes mathematicae},
  year={2004},
  volume={83},
  pages={1-66}
}
  • T. Zaslavsky
  • Published 11 November 2004
  • Mathematics
  • Aequationes mathematicae
A multiary (polyadic, n-ary) quasigroup is an n-ary operation which is invertible with respect to each of its variables. A biased expansion of a graph is a kind of branched covering graph with an additional structure similar to the combinatorial homotopy of circles. A biased expansion of a circle with chords encodes a multiary quasigroup, the chords corresponding to factorizations, i.e., associative structure. Some but not all biased expansions are constructed from groups (group expansions… 
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