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- Alexei G. Myasnikov, Zoran Sunic
- LATA
- 2012

Zoraň Suni´c Cayley graph automatic groups are not necessarily Cayley grap

We study cellular automata on regular rooted trees. This includes the characterization of sofic tree shifts in terms of unrestricted Rabin automata and the decidability of the surjectivity problem for cellular automata between sofic tree shifts.

- ZORAN ŠUNIĆ
- 2006

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)

- Zoran Sunic
- Eur. J. Comb.
- 2007

A connection relating Tamari lattices on symmetric groups regarded as lattices under the weak Bruhat order to the positive monoid P of Thompson group F is presented. Tamari congruence classes correspond to classes of equivalent elements in P. The two well known normal forms in P correspond to endpoints of intervals in the weak Bruhat order that determine… (More)

- Martin R. Bridson, José Burillo, Murray Elder, Zoran Sunic
- IJAC
- 2012

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)

- Zoran Šunić
- 2006

For each prime p and a monic polynomial f , invertible over p, we define a group G p,f of p-adic automorphisms of the p-ary rooted tree. The groups are modeled after the first Grigorchuk group, which in this setting is the group G 2,x 2 +x+1. We show that the constructed groups are self-similar, regular branch groups. This enables us to calculate the… (More)

- Zoran Sunic
- Eur. J. Comb.
- 2012

In the Twin Towers of Hanoi version of the well known Towers of Hanoi Problem there are two coupled sets of pegs. In each move, one chooses a pair of pegs in one of the sets and performs the only possible legal transfer of a disk between the chosen pegs (the smallest disk from one of the pegs is moved to the other peg), but also, simultaneously, between the… (More)

- ZORAN ŠUNIĆ
- 2009

Baer characterized capable finite abelian groups (a group is capable if it is isomorphic to the quotient of some group by its center) by a condition on the size of the factors in the invariant factor decomposition (the group must be noncyclic and the top two invariant factors must be equal). We provide a different characterization, given in terms of a… (More)

- Tullio Ceccherini-Silberstein, Michel Coornaert, Francesca Fiorenzi, Zoran Sunic
- Theor. Comput. Sci.
- 2013

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)

A solution function for convex transferable utility games encourages the grand coalition if no player prefers (in a precise sense defined in the text) any coalition to the grand coalition. We show that the Shapley value encourages the grand coalition in all convex games and the τ-value encourages the grand coalitions in convex games up to three (but not… (More)