We generalize Ringel and Schmidmeier's theory on the Auslander-Reiten
translation of the submodule category S2β(A) to the monomorphism
category Snβ(A). As in the case of n=2, Snβ(A) has
Auslander-Reiten sequences, and the Auslander-Reiten translation
ΟSβ of Snβ(A) can be explicitly formulated via
Ο of A-mod. Furthermore, if A is a selfinjective algebra, we study the
periodicity of ΟSβ on the objects of Snβ(A), and of
the Serre functor FSβ on the objects of the stable monomorphism
category Snβ(A)β. In particular, ΟS2m(n+1)βXβ X for X\in\mathcal{S}_n(\A(m, t)); and FSm(n+1)βXβ X for X\in\underline{\mathcal{S}_n(\A(m, t))}, where
\A(m, t), \ m\ge1, \ t\ge2, are the selfinjective Nakayama algebras.Comment: 33 pages, 1 figure