Invariants of inversive 2-structures on groups of labels

  • Authors:

  • A. Ehrenfeucht;T. Harju;G. Rozenberg

  • Affiliations:

  • Department of Computer Science, University of Colorado at Boulder, Boulder, Co 80309, U.S.A.;Department of Mathematics, University of Turku, FIN-20014 Turku, Finland;Department of Computer Science, University of Colorado at Boulder, Boulder, Co 80309, U.S.A. and Department of Computer Science, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands

  • Venue:
  • Mathematical Structures in Computer Science
  • Year:
  • 1997

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Abstract

For a finite set D of nodes let E2(D)={(x, y)∣x, y∈D, x≠y}. We define an inversive Δ2-structure g as a function gE2(D)→Δ into a given group Δ satisfying the property g(x, y)=g(y, x)−1 for all (x, y)∈E2(D). For each function (selector) σD→Δ there is a corresponding inversive Δ2-structure gσ defined by gσ(x, y)=σ(x)·g(x, y)·σ(y)−1. A function η mapping each g into the group Δ is called an invariant if η(gσ)=η(g) for all g and σ. We study the group of free invariants η of inversive Δ2-structures, where η is defined by a word from the free monoid with involution generated by the set E 2(D). In particular, if Δ is abelian, the group of free invariants is generated by triangle words of the form (x0, x1)(x1, x2)(x2, x0).