In this two parts article with the same main title we study a problem of Coxeter-Gram spectral
analysis of edge-bipartite graphs (bigraphs), a class of signed graphs. We ask for a criterion …

We study edge-bipartite graphs (bigraphs), a class of signed graphs, by means of the
inflation algorithm which relies on performing certain elementary transformations on a given …

Let Λ be a k-algebra of finite global dimension. We study tubular families in the Auslander–
Reiten quiver of the bounded derived category D b (Λ) satisfying certain natural axioms. In …

Each exceptional object M in the category S (6˜) of nilpotent operators with nilpotency
degree bounded by 6, acting on finite dimensional vector spaces with invariant subspaces in …

We present combinatorial algorithms for solving three problems that appear in the study of
the degeneration order≤ deg for the variety of finite-dimensional modules over a k-algebra …

We give a description of matrix bimodules parametrizing all indecomposable homogeneous
Λ-modules with a fixed integral slope over a tubular canonical algebra Λ, for all possible …

We give an algorithmic description of matrix bimodules parametrizing all indecomposable
homogeneous Λ-modules with a fixed slope q over a tubular canonical algebra Λ, for all …

We explicitly describe tree representations of the canonically oriented quiver $\widetilde
{\mathbb {E}} _ {6} $. Recall that tree representations can be exhibited using matrices …

Canonical algebras, introduced by CM Ringel in 1984, play an important role in the
representation theory of finite dimensional algebras. They are equipped with a large contact …

Formulas for the dimension vectors of all objects M in the category S (6~) S(̃6) of nilpotent
operators with nilpotency degree bounded by 6, acting on finite dimensional vector spaces …