Dichotomies for classes of homomorphism problems involving unary functions

On the Complexity of Homomorphism Problems Involving Unary Functions

Computational Complexity of Holant Problems

We propose and explore a novel alternative framework to study the complexity of counting problems, called Holant problems. Compared to counting constraint satisfaction problems (#CSP), it is a refinement with a more explicit role for the constraint functions. Both graph homomorphism and #CSP can be viewed as special cases of Holant problems. We prove complexity dichotomy theorems in this framew...

Complexity Dichotomies of Counting Problems

In order to study the complexity of counting problems, several interesting frameworks have been proposed, such as Constraint Satisfaction Problems (#CSP) and Graph Homomorphisms. Recently, we proposed and explored a novel alternative framework, called Holant Problems. It is a refinement with a more explicit role for constraint functions. Both graph homomorphism and #CSP can be viewed as special...

Fekete-Szeg"o problems for analytic functions in the space of logistic sigmoid functions based on quasi-subordination

In this paper, we define new subclasses ${S}^{*}_{q}(alpha,Phi),$ ${M}_{q}(alpha,Phi)$ and ${L}_{q}(alpha,Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete--Szeg"o inequalities. Further, we discuss the improved ...

Counting Homomorphisms to Trees Modulo a Prime

Many important graph theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular independent sets and colourings. In this article we study the complexity of #pHomsToH, the problem of counting graph homomorphisms from an input graph to a graph H modulo a prime number p. Dyer and Greenhill proved a dichotomy stating t...