Frobenius functions on translation quivers

Istv\'an \'Acoston, Erzs\'ebet Luk\'acs and Claus Michael Ringel

Abstract. Frobenius functions are integral valued functions given on vertices 
of translation quivers and satisfying certain subadditivity conditions. 
Typical examples are the length function and the dimension function on the 
stable Auslander-Reiten quiver of a finite dimensional selfinjective algebra. 
In our paper we study in detail Frobenius functions on the translation quivers 
ZA_\infty, ZA^\infty_\infty and some related ones. In particular we show that 
there is a one-to-one correspondence between Frobenius functions on the stable 
tube T(n) and Frobenius functions on the wing W(n), and we classify them using 
certain related combinatorial structures.