Pairs of partially ordered sets of tame representation type
Let S and T be finite partially ordered sets. It is proved in the paper that the category \({\mathcal R}(S,T)\) of representations of the pair (S,T) is of tame representation type if and only if either one of the posets S, T is linearly ordered (say S is) and the disjoint union poset \(T+S-\{s\}\), where s is maximal in S, does not contain a critical Nazarova poset (1,1,1,1,1), (1,1,1,2), (2,2,3), (1,3,4), (1,2,6), (N,5), or S and T contain the poset (1,1) but neither S nor T contains a subposet of the form (1,1,1), (1,2). Here by m we mean the chain consisting of m vertices and by N we mean \(a\prec b\succ c\prec d\).
scientific article; zbMATH DE number 4077481
scientific article