8 citations · 28 across the 17 of their papers we have counts for
22 papers
On leading Gopakumar--Vafa invariants of local and leading Betti numbers of moduli spaces of one-dimensional sheaves on
Zhiyuan Wang, Chenglang Yang
In this paper we use the topological vertex formalism to derive a structural formula for the leading terms of the generating series of Gromov--Witten invariants of local $\mathbb P…
Generalized Kontsevich model, topological recursion, and -spin theory
Shuai Guo, Ce Ji, Chenglang Yang +1
By employing polynomial-reduced KP integrability, combined with the string equation, this work establishes explicit relationships between the generalized Kontsevich model, the topo…
The -Point Function of -Core Partitions and Topological Vertex
Chenglang Yang
In this paper, we study the -point function of -core partitions. The main tool is the topological vertex, originally developed to study the topological string theory for tori…
Total partition function with fermionic number fluxes of local toric Calabi--Yau threefold and KP integrability
Zhiyuan Wang, Chenglang Yang, Jian Zhou
Aganagic, Dijkgraaf, Klemm, Mariño and Vafa \cite{adkmv} predicted that the open string partition function on a smooth toric Calabi--Yau threefold should be a tau-function of multi…
The structures of simple Hurwitz numbers and monotone Hurwitz numbers with varying genus
Chenglang Yang
We study the structures of ordinary simple Hurwitz numbers and monotone Hurwitz numbers with varying genus. More precisely, we prove that when the ramification type is fixed and th…
The bilinear fermionic form for KP and BKP hierarchies
Shuai Guo, Ce Ji, Chenglang Yang
For a tau-function of the KP or BKP hierarchy, we introduce the notion of lifting operator and derive an equation connecting the corresponding fermionic two-point function and ferm…
Correlation Function of Self-Conjugate Partitions: -Difference Equation and Quasimodularity
Zhiyong Wang, Chenglang Yang
In this paper, we study the uniform measure for the self-conjugate partitions. We derive the -difference equation which is satisfied by the -point correlation function relate…
On -Coefficient Binomial Polynomiality of Hurwitz Numbers and Generalized Dessin Counting
Zhiyuan Wang, Chenglang Yang
In this paper, we study a certain type of Hurwitz numbers which count branched covers over the Riemann sphere admitting several branch points with fixed ramification types, one bra…
Schröder Paths, Their Generalizations and Knot Invariants
Ce Ji, Qian Tang, Chenglang Yang
We study some kinds of generalizations of Schröder paths below a line with rational slope and derive the -difference equations that are satisfied by their generating functions.…
Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures
Chenglang Yang
The symplectic/orthogonal contents of partitions are related to the dimensions of irreducible representations of symplectic/orthogonal groups. In 2012, motivated by Nekrasov--Okoun…
On a Proof of the ADKMV Conjecture -- -KP Integrability of the Topological Vertex
Zhiyuan Wang, Chenglang Yang, Jian Zhou
We present a mathematical proof of the Aganagic-Dijkgraaf-Klemm-Mariño-Vafa Conjecture proposed in 2006, which states that the generating function of the topological vertex, i.e.,…
On two families of Nekrasov-Okounkov type formulas
Chenglang Yang
In this paper, we use the vacuum expectation value formula of the topological vertex and its rotation symmetry to derive two families of Nekrasov-Okounkov type formulas. Each famil…
A remark on certain restricted plane partitions and crystal melting model
Chenglang Yang
In this paper, we provide formulas to calculate the partition functions of two types of plane partitions using the crystal melting model introduced by Okounkov, Reshetikhin and Vaf…
BKP-Affine Coordinates and Emergent Geometry of Generalized Brézin-Gross-Witten Tau-Functions
Zhiyuan Wang, Chenglang Yang, Qingsheng Zhang
Following Zhou's framework, we consider the emergent geometry of the generalized Brézin-Gross-Witten models whose partition functions are known to be a family of tau-functions of t…
Kac-Schwarz Operators of Type , Quantum Spectral Curves, and Spin Hurwitz Numbers
Ce Ji, Zhiyuan Wang, Chenglang Yang
Given a tau-function of the BKP hierarchy satisfying , we discuss the relation between its BKP-affine coordinates on the isotropic Sato Grassmannian and its BKP-wave…
Connected -Point Functions of Diagonal -BKP Tau-Functions, and Spin Double Hurwitz Numbers
Zhiyuan Wang, Chenglang Yang
We derive an explicit formula for the connected -point functions associated to an arbitrary diagonal tau-function of the -BKP hierarchy using computation of neutral fermi…
Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected -Point Functions, and Double Hurwitz Numbers
Zhiyuan Wang, Chenglang Yang
We derive an explicit formula for the connected -point functions associated to an arbitrary diagonal tau-function of the 2d Toda lat…
Action of -type operators on Schur functions and Schur Q-functions
Xiaobo Liu, Chenglang Yang
In this paper, we investigate a series of W-type differential operators, which appear naturally in the symmetry algebras of KP and BKP hierarchies. In particular, they include all…
BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic -Point Functions
Zhiyuan Wang, Chenglang Yang
We derive a formula for the connected -point functions of a tau-function of the BKP hierarchy in terms of its affine coordinates. This is a BKP-analogue of a formula for KP tau-…
Action of Virasoro operators on Hall-Littlewood polynomials
Xiaobo Liu, Chenglang Yang
In this paper, we prove formulas for the action of Virasoro operators on Hall-Littlewood polynomials at roots of unity.
Q-Polynomial expansion for Brezin-Gross-Witten tau-function
Xiaobo Liu, Chenglang Yang
In this paper, we prove a conjecture of Alexandrov that the generalized Brezin-Gross-Witten tau-functions are hypergeometric tau functions of BKP hierarchy after re-scaling. In par…
Schur Q-Polynomials and Kontsevich-Witten Tau Function
Xiaobo Liu, Chenglang Yang
Using matrix model, Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau-function as a linear expansion of Schur Q-polynomials. In this paper, we will…