A graph homomorphism is an edge preserving vertex mapping between two graphs. Locally constrained homomorphisms are those that behave well on the neighborhoods of vertices — if the neighborhood of any vertex of the source graph is mapped bijectively (injectively, surjectively) to the neighborhood of its image in the target graph, the homomorphism is called locally bijective (injective, surjecti...

The stabilizer of a fixed point class of a map is the fixed subgroup of the induced fundamental group homomorphism based at a point in the class. A theorem of Jiang, Wang and Zhang is used to prove that if a map of a graph satisfies a strong remnant condition, then the stabilizers of all its fixed point classes are trivial. Consequently, if φp,f is the nvalued lift to a covering space p of a ma...

Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f ∈ Int(D), we explicitly construct a divisor homomorphism from [[f ]], the divisor-closed submonoid of Int(D) generated by f , to a finite sum of copies of (N0,+). This implies that [[f ]] is a Krull monoid. For V a discrete valuation domain, we give explicit divisor theories of various submonoids of Int(V ...

Ahlswede and Winter [IEEE Trans. Inf. Th. 2002] introduced a Chernoff bound for matrix-valued random variables, which is a non-trivial generalization of the usual Chernoff bound for real-valued random variables. We present an efficient derandomization of their bound using the method of pessimistic estimators (see Raghavan [JCSS 1988]). As a consequence, we derandomize an efficient construction ...

The theory of Boolean algebras can be fruitfully applied to judgment aggregation: Assuming universality, systematicity and a sufficiently rich agenda, there is a correspondence between (i) non-trivial deductively closed judgment aggregators and (ii) Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Furthermore, there is a correspondence between (i) consistent com...

We consider the cohomology of two-dimensional subshifts, and develop a new approach to proving that every cocycle is trivial (i.e. cohomologous to a homomorphism). We introduce semi-safe subshifts which, roughly speaking, have the property that some symbol can surround all allowed blocks in at least one horizontal and one vertical direction. We prove that for such subshifts, every locally const...

Let K be a finite extension of the p-adic field Qp and let F (X,Y ) and G(X, Y ) be one-dimensional formal group laws over the ring of integers OK of K. Let φ(X) be a homomorphism from F to G which is defined over the ring of integers OCp of the completion Cp of Q p . In this paper we prove that if ker(φ) is finite then there is a discretely valued subfield L ⊂ Cp such that φ(X) is defined over...

For any real inner product space V , let T (V ) denote its tensor algebra. We give a theorem giving conditions under which a real-valued algebra homomorphism from certain subalgebras of T (V ) can be extended to T (V ). The main applications are characterizations of combinatorial parameters by means of ‘reflection positivity’. The proof method follows mainly that of Szegedy [4], whose theorem i...

Let f be a real-valued real analytic function in several variables. Then we associate with each algebraic local cohomology class u with support in f = 0 a distribution (generalized function) ρ(u) in terms of the residue of fλ + with respect to λ at a negative integer. Then ρ constitutes a homomorphism of modules over the sheaf of analtyic functions but not over the sheaf of differential operato...

Graph homomorphism has been studied intensively. Given an m ×m symmetric matrix A, the graph homomorphism function is defined as