This paper is concerned with the existence of consecutive pairs and triples multiplicatively dependent integers. A theorem by LeVeque on Pillai's equation implies that only integers larger than 1 are (2,8) (3,9). For triples, we prove following theorem: If a∉{2,8} a fixed integer 1, then there finitely many (a,b,c) pairwise distinct such (a,b,c), (a+1,b+1,c+1) (a+2,b+2,c+2) each dependent. More...

We study the relations between Multi-valued Decision Diagrams (MDD) and tuples (i.e. elements of the Cartesian Product of variables). First, we improve the existing methods for transforming a set of tuples, Global Cut Seeds, sequences of tuples into MDDs. Then, we present some in-place algorithms for adding and deleting tuples from an MDD. Next, we consider an MDD constraint which is modified d...

The Weisfeiler-Leman procedure is a widely-used technique for graph isomorphism testing that works by iteratively computing an isomorphism-invariant coloring of vertex tuples. Meanwhile, fundamental tool in structural theory, which often exploited approaches to tackle the problem, decomposition into 2- and 3-connected components. We prove 2-dimensional algorithm implicitly computes its This imp...