A knot in a solid torus defines map on the set of (smooth or topological) concordance classes knots S 3 S^3 ...

Discovering new integer sequences and generalizing the existing ones are important and of great interest. In this article, various balanced k-ary trees are first studied and their taxonomy is built. In particular, two systematic balanced k-ary trees, whose nth tree is determined by a certain algorithm, are identified, i.e., complete and sizebalanced k-ary trees. The integer sequences from the f...

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...

We study homomorphisms between randomly directed paths and give estimates on the probability of the existence of such homomorphism. We show that a random path is a core with positive probability. We apply our results in the investigation of homomorphism dualities, the most natural situation when a homomorphism (or Constraint Satisfaction) problem is in coNP.

In this paper, we generalize some existing results on Boolean functions to the q-ary functions defined over Zq, where q ≥ 2 is an integer, and obtain some new characterization of q-ary functions based on spectral analysis. We provide a relationship between WalshHadamard spectra of two p-ary functions f and g (for p a prime) and their derivative Df,g. We provide a relationship between the Walsh-...

Given two graphs G = (VG, EG) and H = (VH , EH), a homomorphism from G to H is a function f : VG → VH such that for every uv ∈ EG, f(u)f(v) ∈ EH . A homomorphism from G to H is referred to as an H-colouring of G and the vertices of H are regarded as colours. The graph H is called the target of the homomorphism. These definitions extend to directed graphs by requiring that the mapping must prese...

Partee (1986) claimed without proof that the function BE is the only homomorphism that makes the Partee triangle commute. This paper shows that this claim is incorrect unless “homomorphism” is understood as “complete homomorphism.” It also shows that BE and A are the inverses of each other on certain natural assumptions.