We generalize the concept of a cycle from graphs to simplicial complexes. We show that a simplicial cycle is either a sequence of facets connected in the shape of a circle, or is ...
We show that the hitting time of the discrete time quantum random walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential ...
In previous work [14] I introduced a generalised notion of coalgebra that is capable of modelling binary methods as they occur in object-oriented programming. An important problem...
This paper deals with the problem of constructing Steiner trees of minimum weight with diameter bounded by d, spanning a given set of vertices in a graph. Exact solutions or logar...
In this paper we analyze O’Hara’s partition bijection. We present three type of results. First, we show that O’Hara’s bijection can be viewed geometrically as a certain sci...