We present new generalizations of Olson’s theorem and of a consequence of Alon’s Combinatorial Nullstellensatz. These enable us to extend some of their combinatorial applications with conditions modulo primes to conditions modulo prime powers. We analyze computational search problems corresponding to these kinds of combinatorial questions and we prove that the problem of finding degreeconstrain...

We derive combinatorial necessary conditions for discrete-time quantum walks defined by regular mixed graphs to be periodic. If the walk is periodic, all eigenvalues of time evolution matrices must algebraic integers. Focusing on this, we explore which ring coefficients characteristic polynomials should belong to. On other hand, $\eta$-Hermitian adjacency have implications. From these, can find...

Background: Post-translational modifications of histone residue tails are an important component of genome regulation. It is becoming increasingly clear that the combinatorial presence and absence of various modifications define discrete chromatin states which determine the functional properties of a locus. An emerging experimental goal is to track changes in chromatin state maps across differe...

Dynamic combinatorial chemistry has emerged as a promising tool for the discovery of complex receptors in supramolecular chemistry. At the heart of dynamic combinatorial chemistry are the reversible reactions that enable the exchange of building blocks between library members in dynamic combinatorial libraries (DCLs) ensuring thermodynamic control over the system. If more than one reversible re...

The analogy between combinatorial optimization and statistical mechanics has proven to be a fruitful object of study. Simulated annealing, a metaheuristic for combinatorial optimization problems, is based on this analogy. In this paper we use the statistical mechanics formalism based on the above mentioned analogy to analyze the asymptotic behavior of a special class of combinatorial optimizati...