13 citations · 51 across the 20 of their papers we have counts for
23 papers
Low-degree filtrations in ordinary and Lagrangian Grassmannian cohomology
Huan Xiong
We prove the Hilbert-series formulas conjectured by Reiner--Tudose and by the Polymath Jr. Grassmannian group for the subalgebras of ordinary and Lagrangian Grassmannian cohomology…
A Local Approximation Characterization of Oka Manifolds
Sicheng An, Yun-Heng Du, Bin Guo +2
We introduce the local approximation propert (LAP) and prove that it characterizes Oka manifolds. We prove that LAP yields convex approximation and, in an -dimensional target, p…
On the distributions of the statistics (des, maj, inv) over several classes of permutations
Guo-Niu Han, Kathy Q. Ji, Huan Xiong
We investigate the joint distribution of the trivariate statistics (des, maj, inv) on classical permutations, Andre permutations of the first and second kinds, and Simsun permutati…
The 1/2-Conjecture for -Binomial Coefficients with Fractional Index
Guo-Niu Han, Huan Xiong
For a nonnegative integer and a rational number , we define the generalized Gaussian binomial coefficient $\qbinom{r+k}{k} = \frac{(q^{r+1}; q)_k}{(q; q)_k}$.…
Proof of a Conjecture of Nath and Sellers on Simultaneous Core Partitions
Yetong Sha, Huan Xiong
In 2016, Nath and Sellers proposed a conjecture regarding the precise largest size of -core partitions. In this paper, we prove their conjecture. One of the key te…
Deep ReLU Networks Have Surprisingly Simple Polytopes
Feng-Lei Fan, Wei Huang, Xiangru Zhong +4
A ReLU network is a piecewise linear function over polytopes. Figuring out the properties of such polytopes is of fundamental importance for the research and development of neural…
Zeroth-Order Negative Curvature Finding: Escaping Saddle Points without Gradients
Hualin Zhang, Huan Xiong, Bin Gu
We consider escaping saddle points of nonconvex problems where only the function evaluations can be accessed. Although a variety of works have been proposed, the majority of them r…
Combinatorics of Integer Partitions With Prescribed Perimeter
Zhicong Lin, Huan Xiong, Sherry H. F. Yan
We prove that the number of even parts and the number of times that parts are repeated have the same distribution over integer partitions with a fixed perimeter. This refines Strau…
Monotonicity properties for ranks of overpartitions
Huan Xiong, Wenston J. T. Zang
The rank of partitions play an important role in the combinatorial interpretations of several Ramanujan's famous congruence formulas. In 2005 and 2008, the -rank and -rank…
On the polynomiality and asymptotics of moments of sizes for random -core partitions with distinct parts
Huan Xiong, Wenston J. T. Zang
Amdeberhan's conjectures on the enumeration, the average size, and the largest size of -core partitions with distinct parts have motivated many research on this topic. Rec…
Polynomiality of certain average weights for oscillating tableaux
Guo-Niu Han, Huan Xiong
We prove that a family of average weights for oscillating tableaux are polynomials in two variables, namely, the length of the oscillating tableau and the size of the ending partit…
On the largest sizes of certain simultaneous core partitions with distinct parts
Huan Xiong
Motivated by Amdeberhan's conjecture on -core partitions with distinct parts, various results on the numbers, the largest sizes and the average sizes of simultaneous core…
Some useful theorems for asymptotic formulas and their applications to skew plane partitions and cylindric partitions
Guo-Niu Han, Huan Xiong
Inspired by the works of Dewar, Murty and Kotěšovec, we establish some useful theorems for asymptotic formulas. As an application, we obtain asymptotic formulas for the numbers of…
Skew doubled shifted plane partitions: calculus and asymptotics
Guo-Niu Han, Huan Xiong
Plane partitions have been widely studied in Mathematics since MacMahon. See, for example, the works by Andrews, Macdonald, Stanley, Sagan and Krattenthaler. The Schur process appr…
Polynomiality of some hook-content summations for doubled distinct and self-conjugate partitions
Guo-Niu Han, Huan Xiong
In 2009, the first author proved the Nekrasov-Okounkov formula on hook lengths for integer partitions by using an identity of Macdonald in the framework of type affi…
New hook-content formulas for strict partitions
Guo-Niu Han, Huan Xiong
We introduce the difference operator for functions defined on strict partitions and prove a polynomiality property for a summation involving the hook length and content statistics.…
Difference operators for partitions under the Littlewood decomposition
Paul-Olivier Dehaye, Guo-Niu Han, Huan Xiong
The concept of -difference operator for functions of partitions is introduced to prove a generalization of Stanley's theorem on polynomiality of Plancherel averages of symmetric…
Core partitions with distinct parts
Huan Xiong
Simultaneous core partitions have attracted much attention since Anderson's work on the number of -core partitions. In this paper we focus on simultaneous core partition…
Finite Groups Whose Character Graphs Associated with Codegrees Have No Triangles
Huan Xiong
Motivated by the Problem proposed by Y. Berkovich and E. Zhmud' in their book "Characters of finite groups, Part ", we give a characterization of finite groups whose irred…
Difference operators for partitions and some applications
Guo-Niu Han, Huan Xiong
Motivated by the Nekrasov-Okounkov formula on hook lengths, the first author conjectured that the Plancherel average of the -th power sum of hook lengths of partitions with siz…
Partitions with the same hook multiset
Huan Xiong
It is well-known that two conjugate partitions have the same hook multiset. But two different partitions with the same hook multiset may not be conjugate to each other. In ,…
The number of simultaneous core partitions
Huan Xiong
Amdeberhan conjectured that the number of -core partitions is . In this paper, we obtain the…
On the largest size of -core partitions
Huan Xiong
In this paper we prove that Amdeberhan's conjecture on the largest size of -core partitions is true. We also show that the number of -core partiti…