We prove a complexity dichotomy for Holant problems on the boolean domain with arbitrary
sets of real-valued constraint functions. These constraint functions need not be symmetric …

Graph homomorphism has been an important research topic since its introduction [20].
Stated in the language of binary relational structures in that paper [20], Lovász proved a …

We study the computational complexity of counting weighted Eulerian orientations, denoted
as# EO problems. We prove a complexity dichotomy theorem for# EO defined by a set of …

Holant problems are intimately connected with quantum theory as tensor networks. We first
use techniques from Holant theory to derive new and improved results for quantum …

We discover a novel connection between two classical mathematical notions, Eulerian
orientations and Hadamard codes by studying the counting problem of Eulerian orientations …

We discover new P-time computable six-vertex models on planar graphs beyond
Kasteleyn's algorithm for counting planar perfect matchings.∗ We further prove that there are …

Holant problems are intimately connected with quantum theory as tensor networks. We first
use techniques from Holant theory to derive new and improved results for quantum …

This dissertation furthers a systematic study of the complexity classification of counting
problems. A central goal of this study is to prove complexity classification theorems which …

We prove a complexity dichotomy theorem for the eight-vertex model. For every setting of the
parameters of the model, we prove that computing the partition function is either solvable in …