Minimum cost homomorphism problems can be viewed as a generalization of list homomorphism problems. They also extend two well-known graph colouring problems: the minimum colour sum problem and the optimum cost chromatic partition problem. In both of these problems, the cost function meets an additional constraint: the cost of using a specific colour is the same for every vertex of the input gra...

The well-known third list homomorphism theorem states that if a function h is both an instance of foldr and foldl , it is a list homomorphism. Plenty of previous works devoted to constructing list homomorphisms, however, overlook the fact that proving h is both a foldr and a foldl is often the hardest part which, once done, already provides a useful hint about what the resulting list homomorphi...

We note how several central results in multiplicative number theory may be rephrased naturally in terms of multiplicative functions f that pretend to be another multiplicative function g. We formalize a ‘distance’ which gives a measure of such pretentiousness, and as one consequence obtain a curious inequality for the zeta-function. A common theme in several problems in multiplicative number th...

The paper examines multiplicative ergodic theorems and the related multiplicative Poisson equation for an irreducible Markov chain on a countable state space. The partial products are considered for a realvalued function on the state space. If the function of interest satisfies a monotone condition, or is dominated by such a function, then (i) The mean normalized products converge geometrically...