7 papers
Rectangular Cyclotomic Expansions of Colored HOMFLY-PT Polynomials
Honghuai Fang, Tian Zhou
We prove the rectangular cyclotomic expansion conjecture of Kameyama, Nawata, Tao, and Zhang for reduced colored HOMFLY-PT polynomials of arbitrary zero-framed knots. We also prove…
Cyclotomic Newton Expansions and a Rank-Uniform Integer-Valued Newton Completion
Honghuai Fang, Tian Zhou
Let denote the reduced quantum invariant of a zero-framed knot , colored by the th symmetric power of the defining representation and normalized to…
On Hamilton cycles in connected vertex-transitive graphs of order
Zhou Tianlei
The existence of Hamilton cycles in connected vertex-transitive graphs is a core open problem in algebraic graph theory, originating from Lovász's 1969 conjecture. All connected ve…
Geometry of Unimodular Random Hyperbolic Polyhedra
Huabin Ge, Yangxiang Lu, Chuwen Wang +1
We develop a geometric and probabilistic theory of unimodular random infinite trivalent hyperbolic polyhedra in , allowing ordinary, ideal, and hyperideal vertices. O…
Random infinite ideal angled graphs and ideal hyperbolic polyhedra
Huabin Ge, Yangxiang Lu, Chuwen Wang +1
This article aims to develop the theory of random infinite ideal hyperbolic polyhedra (abbr. IHP) from multiple perspectives, including combinatorics, geometry, analysis, and rando…
Hamilton cycles in vertex-transitive graphs of order
Shaofei Du, Tianlei Zhou
It was shown by Kutnar and \v Sparl in 2009 that every connected vertex-transitive graph of order , where is a prime, contains a Hamilton path. In this paper, it will be sh…
The characterizing properties of (signless) Laplacian permanental polynomials of bicyclic graphs
Tingzeng Wu, Tian Zhou
Let be a graph with vertices, and let and be the Laplacian matrix and signless Laplacian matrix of , respectively. The polynomial $π(L(G);x)={\rm per}(xI-L…