On representation type of a pair of posets with involution - Bondarenko, V.M. (Algebra and Discrete Mathematics, 2005)
In this paper we consider the problem on classifying the representations of a pair of posets with involution. We
prove that if one of these is a chain of length at least 4 with trivial
involution and the other is with nontrivial one, then the pair is
tame ⇔ it is of finite type ⇔ the poset with nontrivial involution
is a ∗-semichain (∗ being the involution). The case that each of the
posets with involution is not a chain with trivial one was considered by the author earlier. In proving our result we do not use the
known technically difficult results on representation type of posets
with involution.