Zoran Sunic

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Let a and b be positive, relatively prime integers. We show that the following are equivalent: (i) d is a dead end in the (symmetric) Cayley graph of Z with respect to a and b, (ii) d is a Frobenius value with respect to a and b (it cannot be written as a non-negative or non-positive integer linear combination of a and b), and d is maximal (in the Cayley(More)
This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely generated group G has an element whose normal closure is abelian and of finite index, then G has a finite generating set(More)
We study the sofic tree shifts of A Σ * , where Σ * is a regular rooted tree of finite rank. In particular, we give their characterization in terms of unrestricted Rabin automata. We show that if X ⊂ A Σ * is a sofic tree shift, then the configurations in X whose orbit under the shift action is finite are dense in X, and, as a consequence of this, we deduce(More)
We introduce the notion of a normal gallery, a gallery in which any configuration of guards that visually covers the walls necessarily covers the entire gallery. We show that any star gallery is normal and any gallery with at most two reflex corners is normal. A polynomial time algorithm is provided deciding if, for a given gallery and a finite set of(More)