# Cerny's conjecture, synchronizing automata, group representation theory - Mathematics > Combinatorics

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Abstract: Let us say that a Cayley graph $\Gamma$ of a group $G$ of order $n$ is aCerny Cayley graph if every synchronizing automaton containing $\Gamma$ as asubgraph with the same vertex set admits a synchronizing word of length at most$n-1^2$. In this paper we use the representation theory of groups over therational numbers to obtain a number of new infinite families of {\v{C}}ern{\-y}Cayley graphs.

Author: ** Benjamin Steinberg**

Source: https://arxiv.org/