25 citations · 60 across the 23 of their papers we have counts for
24 papers
A polynomial invariant of planar curves
Zhiyun Cheng, Yin Tian, Tianyu Yuan
We construct a polynomial invariant of planar curves via skein relations, which generalizes Arnold's numerical invariant .
GL-racks and coloring invariants of Legendrian knots
Zhiyun Cheng, Zhiyi He
In this paper, we explore the algebraic structure of GL-racks, and demonstrate that finite GL-racks decompose canonically into permutation GL-racks and block GL-racks. As a corolla…
Coloring invariants for links in
Zhiyun Cheng, Hongzhu Gao
Let be a closed oriented surface of genus , in this paper we discuss how to define coloring invariants and its generalizations for links in .
Intersection graph and writhe polynomial
Zhiyun Cheng
We prove that two virtual knots have equivalent intersection graphs if and only if they have the same writhe polynomial.
Region crossing change on planar trivalent graphs
Zhiyun Cheng
In this short note, we investigate the effect of region crossing change on planar trivalent graphs.
Chord index for knots in thickened surfaces
Zhiyun Cheng, Hongzhu Gao, Mengjian Xu
In this note, we construct a chord index homomorphism from a subgroup of to the group of chord indices of a knot in . Some knot invariants deriv…
A categorification for the signed chromatic polynomial
Zhiyun Cheng, Ziyi Lei, Yitian Wang +1
By coloring a signed graph by signed colors, one obtains the signed chromatic polynomial of the signed graph. For each signed graph we construct graded cohomology groups whose grad…
Region crossing change on surfaces
Jiawei Cheng, Zhiyun Cheng, Jinwen Xu +1
Region crossing change is a local operation on link diagrams. The behavior of region crossing change on is well understood. In this paper, we study the behavior of (modified)…
Some remarks on the chord index
Zhiyun Cheng, Hongzhu Gao, Mengjian Xu
In this paper we discuss how to define a chord index via smoothing a real crossing point of a virtual knot diagram. Several polynomial invariants of virtual knots and links can be…
A note on the writhe polynomial and the virtual crossing number
Zhiyun Cheng
In this note we give a new lower bound on the virtual crossing number via the writhe polynomial, which refines a result of B. Mellor. The proof is based on a new interpretation of…
On the Classification of Topological Quandles
Zhiyun Cheng, Mohamed Elhamdadi, Boris Shekhtman
We investigate the classification of topological quandles on some simple manifolds. Precisely we classify all Alexander quandle structures, up to isomorphism, on the real line and…
Rooted trees with the same plucking polynomial
Zhiyun Cheng, Sujoy Mukherjee, Jozef Przytycki +2
In this paper we give a sufficient and necessary condition for two rooted trees with the same plucking polynomial. Furthermore, we give a criteria for a sequence of non-negative in…
The chord index, its definitions, applications and generalizations
Zhiyun Cheng
In this paper we study the chord index of virtual knots, which can be thought of as an extension of the chord parity. We show how to use the chord index to define finite type invar…
Strict unimodality of q-polynomials of rooted trees
Zhiyun Cheng, Sujoy Mukherjee, Jozef H. Przytycki +2
We classify rooted trees which have strictly unimodal q-polynomials (plucking polynomial). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize res…
A transcendental function invariant of virtual knots
Zhiyun Cheng
In this work we describe a new invariant of virtual knots. We show that this transcendental function invariant generalizes several polynomial invariants of virtual knots, such as t…
On Marked Braid Groups
Denis Fedoseev, Vassily Manturov, Zhiyun Cheng
In the present paper, we introduce -braids and, more generally, -braids for an arbitrary group . They form a natural group-theoretic counterpart of -knots, s…
Integral positive (negative) quandle cocycle invariants are trivial for knots
Zhiyun Cheng, Hongzhu Gao
In this note we prove that for any finite quandle and any 2-cocycle $ϕ\in Z^2_{Q\pm}(X; \mathds{Z})$, the cocycle invariant is trivial for all knots .
Bowling ball representation of virtual string links
Zhiyun Cheng
In this paper we investigate the virtual string links via a probabilistic interpretation. This representation can be used to distinguish some virtual string links from classical st…
Positive quandle homology and its applications in knot theory
Zhiyun Cheng, Hongzhu Gao
Algebraic homology and cohomology theories for quandles have been studied extensively in recent years. With a given quandle 2(3)-cocycle one can define a state-sum invariant for kn…
Kauffman-Harary conjecture for alternating virtual knots
Zhiyun Cheng
In 1999, Kauffman-Harary conjectured that every non-trivial Fox -coloring of a reduced, alternating knot diagram with prime determinant is heterogeneous. Ten years later thi…
A polynomial invariant of virtual links
Zhiyun Cheng, Hongzhu Gao
In this paper, we define some polynomial invariants for virtual knots and links. In the first part we use Manturov's parity axioms to obtain a new polynomial invariant of virtual k…
A polynomial invariant of virtual knots
Zhiyun Cheng
The aim of this paper is to introduce a polynomial invariant for virtual knots. We show that can be used to distinguish some virtual knot from its inverse and mir…
When is region crossing change an unknotting operation?
Zhiyun Cheng
In this paper, we prove that region crossing change on a link diagram is an unknotting operation if and only if the link is proper. A description of the behavior of region crossing…
On region crossing change and incidence matrix
Zhiyun Cheng, Hongzhu Gao
In a recent work of Ayaka Shimizu, she defined an operation named region crossing change on link diagrams, and showed that region crossing change is an unknotting operation…