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 algorithms that construct an invertible matrix B∈ M n (Z) that defines congruence B
tr· X· B= Y of given square rational matrices X, Y∈ M n (Q). We describe a general algorithm …

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 find an algorithmic procedure that enables the computation and description of the
structure of the isotropy subgroups of the group of complex orthogonal matrices with respect …

Bidirected graphs are multigraphs where every edge has an independent direction at each
end. In the paper, with an arbitrary bidirected graph we associate a non-negative integral …

Following a Coxeter spectral analysis problems for positive edge-bipartite graphs (signed
multigraphs with a separation property) introduced in Simson (2013)[41] and Simson …

Skew-symmetrizable matrices play an essential role in the classification of cluster algebras.
We prove that the problem of assigning a positive definite quasi-Cartan companion to a …

We present a procedure which enables the computation and the description of structures of
isotropy subgroups of the group of complex orthogonal matrices with respect to the action of …