Abstract: This paper proposes a novel representation of decomposable graphs based on semi-latent tree-dependent bipartite graphs. The novel representation has two main benefits. First, it enables a form of subclustering within maximal cliques of the graph, adding informational richness to the general use of decomposable graphs that could be harnessed in applications with behavioural type of dat...

Abstract The algebraic stability theorem for persistence modules is a central result in the theory of persistent homology. We introduce new proof technique which we use to prove n -dimensional rectangle decomposable up constant $$2n-1$$ 2 n - 1 </m...

For homogeneous decomposable forms F (X) in n variables with integer coefficients, we consider the number of integer solutions x ∈ Zn to the inequality |F (x)| ≤ m as m → ∞. We give asymptotic estimates which improve on those given previously by the author in [T1]. Here our error terms display desirable behaviour as a function of the height whenever the degree of the form and the number of vari...

We show that recursive circulant G(cd m ; d) is hamiltonian decomposable. Recursive circulant is a graph proposed for an interconnection structure of multicomputer networks in [8]. The result is not only a partial answer to the problem posed by Alspach that every connected Cayley graph over an abelian group is hamiltonian decomposable, but also an extension of Micheneau's that recursive circula...