With any symmetrizable integer Cartan matrix C∈ SC arn⊆ M n (Z), a Z-invertible Coxeter
matrix Cox C∈ M n (Z) is associated. We study such positive definite matrices up to a strong …

We formulate a simple model for the bounded derived category of gentle algebras in terms
of marked ribbon graphs and their walks, in order to analyze indecomposable objects …

Cartan matrices and quasi-Cartan matrices play an important role in such areas as Lie
theory, representation theory, and algebraic graph theory. It is known that each (connected) …

We continue the Coxeter spectral study of finite positive edge-bipartite signed (multi) graphs
Δ (bigraphs, for short), with n≥ 2 vertices started in Simson (2013)[44] and developed in …

We study a class of signed graphs called finite connected loop-free edge-bipartite graphs Δ
(bigraphs, for short), started in Simson (2013) and continued in Simson and Zając (2017) …

In the context of signed line graphs, this article introduces a modified inflation technique to
study strong Gram congruence of non-negative (integral quadratic) unit forms, and uses it to …

We study integral quadratic forms in the sense of Roiter, that is, quadratic forms whose
integer coefficients satisfy certain divisibility condition assuring that the associated Weyl …

Following a general framework of Coxeter spectral analysis of signed graphs Δ and finite
posets I introduced by Simson (SIAM J. Discrete Math. 27: 827–854, 2013) we present …

Cartan matrices, quasi-Cartan matrices and associated upper triangular Gram matrices
control important combinatorial aspects of Lie theory and representation theory of …

We consider subsets of linearly independent roots in a certain root system $\varPhi $. Let $
S'$ be such a subset, and let $ S'$ be associated with any Carter diagram $\Gamma'$. The …