arXiv subjects

Ming Yao

Publications and source records attributed to Ming Yao.

9 recordsLinked to original sources

arXiv2026

Non-vanishing of Single, Double, and Triple Schubert Structure Constants

The Schubert vanishing problem asks whether the single Schubert coefficients $c_{u,v}^w$ are zero. In this paper, we consider the non-vanishing problems of double Schubert coefficients $c_{u,v}^w(t)$ and triple Schubert coefficients $c_{u,v}^w(t;y)$. We show that the non-vanishing of $c_{u,v}^w(t;y)$ is completely determined by the non-vanishing of single Schubert coefficients. As a byproduct, we obtain the saturation property of the triple Littlewood--Richardson coefficients $c_{\lambda,\mu}^\nu(t;y)$. Moreover, we pose a conjecture asserting that the non-vanishing of $c_{u,v}^w(t)$ is also determined by the non-vanishing of single or triple Schubert coefficients. We prove a one-side inclusion of the conjecture. For the reverse inclusion, we show that the conjecture holds for the following three cases: the Pieri case, the separated descents case, and the inverse Grassmannian case.

math.CO↗

arXiv2026

Equivariant Schubert Calculus for Inverse Grassmannian Permutations

We give a Graham-positive expansion for the product of two double Schubert polynomials indexed by two inverse Grassmannian permutations. Surprisingly, the nonzero structure constants are double Schubert polynomials in two disjoint sets of equivariant variables. We also give a positive expansion for the product of two single Schubert polynomials indexed by a $321$-avoiding permutation (e.g., a Grassmannian permutation) and an inverse Grassmannian permutation. Unexpectedly, the nonzero structure constants are Edelman--Greene coefficients.

math.CO↗

arXiv2025

Bumpless Pipe Dream Fragments -- Equivariant Geometry of Clans

In this paper, we establish a new geometric setting for bumpless pipe dreams and double Schubert polynomials. Building on the notion of bumpless pipe dream fragments, we define clan polynomials as their weight generating functions. It turns out that clan polynomials arise naturally in the equivariant geometry of ($GL_p\times GL_q$)-orbits over the flag variety $Fl_{p+q}$ parametrized by $(p,q)$-clans. Furthermore, we show that the coefficients in the equivariant Schubert expansion of the fundamental classes of ($GL_p\times GL_q$)-orbit closures are exactly clan polynomials, which resolves an open problem posed by Wyser and Yong.

math.CO↗

arXiv2025

Communication Efficient Multiparty Private Set Intersection from Multi-Point Sequential OPRF

Multiparty private set intersection (MPSI) allows multiple participants to compute the intersection of their locally owned data sets without revealing them. MPSI protocols can be categorized based on the network topology of nodes, with the star, mesh, and ring topologies being the primary types, respectively. Given that star and mesh topologies dominate current implementations, most existing MPSI protocols are based on these two topologies. However, star-topology MPSI protocols suffer from high leader node load, while mesh topology protocols suffer from high communication complexity and overhead. In this paper, we first propose a multi-point sequential oblivious pseudorandom function (MP-SOPRF) in a multi-party setting. Based on MP-SOPRF, we then develop an MPSI protocol with a ring topology, addressing the challenges of communication and computational overhead in existing protocols. We prove that our MPSI protocol is semi-honest secure under the Hamming correlation robustness assumption. Our experiments demonstrate that our MPSI protocol outperforms state-of-the-art protocols, achieving a reduction of 74.8% in communication and a 6% to 287% improvement in computational efficiency.

cs.CR↗

arXiv2025

Valuative Invariants of Catalan Matroids

We decompose the indicator function of each $(a, b)$-Catalan matroid polytope as a weighted sum of indicator function of matroid polytopes that correspond to direct sums of uniform matroids. Catalan matroids lie in the interior of the convex hull of direct sums of uniform matroids in the polytope of all matroids introduced by Ferroni and Fink. Moreover, we describe combinatorially the coefficients of the convex combination of direct sums of uniform matroid corresponding to an $(a,b)$-Catalan matroid. In particular, this allows us to derive explicit formulas for arbitrary valuative invariants of $(a, b)$-Catalan matroids. Among other applications, we prove that $(a,b)$-Catalan matroids are Ehrhart positive, and we find formulas for the Kazhdan--Lusztig invariants of these matroids.

math.CO↗

arXiv2024

P4GCN: Vertical Federated Social Recommendation with Privacy-Preserving Two-Party Graph Convolution Network

In recent years, graph neural networks (GNNs) have been commonly utilized for social recommendation systems. However, real-world scenarios often present challenges related to user privacy and business constraints, inhibiting direct access to valuable social information from other platforms. While many existing methods have tackled matrix factorization-based social recommendations without direct social data access, developing GNN-based federated social recommendation models under similar conditions remains largely unexplored. To address this issue, we propose a novel vertical federated social recommendation method leveraging privacy-preserving two-party graph convolution networks (P4GCN) to enhance recommendation accuracy without requiring direct access to sensitive social information. First, we introduce a Sandwich-Encryption module to ensure comprehensive data privacy during the collaborative computing process. Second, we provide a thorough theoretical analysis of the privacy guarantees, considering the participation of both curious and honest parties. Extensive experiments on four real-world datasets demonstrate that P4GCN outperforms state-of-the-art methods in terms of recommendation accuracy.

cs.SI↗

arXiv2022

EFMVFL: An Efficient and Flexible Multi-party Vertical Federated Learning without a Third Party

Federated learning allows multiple participants to conduct joint modeling without disclosing their local data. Vertical federated learning (VFL) handles the situation where participants share the same ID space and different feature spaces. In most VFL frameworks, to protect the security and privacy of the participants' local data, a third party is needed to generate homomorphic encryption key pairs and perform decryption operations. In this way, the third party is granted the right to decrypt information related to model parameters. However, it isn't easy to find such a credible entity in the real world. Existing methods for solving this problem are either communication-intensive or unsuitable for multi-party scenarios. By combining secret sharing and homomorphic encryption, we propose a novel VFL framework without a third party called EFMVFL, which supports flexible expansion to multiple participants with low communication overhead and is applicable to generalized linear models. We give instantiations of our framework under logistic regression and Poisson regression. Theoretical analysis and experiments show that our framework is secure, more efficient, and easy to be extended to multiple participants.

cs.LG↗

arXiv2019

Using Chinese Characters To Generate Text-Based Passwords For Information Security

Graphical passwords (GPWs) are in many areas of the current world. Topological graphic passwords (Topsnut-gpws) are a new type of cryptography, and they differ from the existing GPWs. A Topsnut-gpw consists of two parts: one is a topological structure (graph), and one is a set of discrete elements (a graph labelling, or coloring), the topological structure connects these discrete elements together to form an interesting "story". Our idea is to transform Chinese characters into computer and electronic equipments with touch screen by speaking, writing and keyboard for forming Hanzi-graphs and Hanzi-gpws. We will use Hanzigpws to produce text-based passwords (TB-paws). We will introduce flawed graph labellings on disconnected Hanzi-graphs.

cs.IT↗

arXiv2015

Probing Graph Proper Total Colorings With Additional Constrained Conditions

Graph colorings are becoming an increasingly useful family of mathematical models for a broad range of applications, such as time tabling and scheduling, frequency assignment, register allocation, computer security and so on. Graph proper total colorings with additional constrained conditions have been investigated intensively in the last decade year. In this article some new graph proper total colorings with additional constrained conditions are defined, and approximations to the chromatic numbers of these colorings are researched, as well as some graphs having these colorings have been verified.

math.CO↗