惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

H
Help Net Security
T
ThreatConnect
SecWiki News
SecWiki News
F
Future of Privacy Forum
AWS News Blog
AWS News Blog
C
Cisco Blogs
A
Arctic Wolf
Vercel News
Vercel News
The GitHub Blog
The GitHub Blog
Scott Helme
Scott Helme
V
V2EX
博客园 - 叶小钗
阮一峰的网络日志
阮一峰的网络日志
K
Kaspersky official blog
G
Google Developers Blog
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
P
Privacy International News Feed
C
Cyber Attacks, Cyber Crime and Cyber Security
N
News | PayPal Newsroom
Schneier on Security
Schneier on Security
NISL@THU
NISL@THU
Microsoft Azure Blog
Microsoft Azure Blog
量子位
The Hacker News
The Hacker News
Stack Overflow Blog
Stack Overflow Blog
Security Latest
Security Latest
M
Microsoft Research Blog - Microsoft Research
Google Online Security Blog
Google Online Security Blog
博客园_首页
C
CXSECURITY Database RSS Feed - CXSecurity.com
I
InfoQ
Google DeepMind News
Google DeepMind News
Y
Y Combinator Blog
The Cloudflare Blog
Microsoft Security Blog
Microsoft Security Blog
Martin Fowler
Martin Fowler
Cisco Talos Blog
Cisco Talos Blog
钛媒体:引领未来商业与生活新知
钛媒体:引领未来商业与生活新知
T
Troy Hunt's Blog
F
Fox-IT International blog
S
Security @ Cisco Blogs
博客园 - 司徒正美
cs.CV updates on arXiv.org
cs.CV updates on arXiv.org
C
Comments on: Blog
Threat Intelligence Blog | Flashpoint
Threat Intelligence Blog | Flashpoint
L
LINUX DO - 最新话题
GbyAI
GbyAI
Project Zero
Project Zero
腾讯CDC
T
Tailwind CSS Blog

math updates on arXiv.org

Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions Improving the Accuracy of the Exponentially Fitted Scheme on Piecewise Uniform Meshes TriVAL: A Tri-Validation Framework for Faithful Automatic Optimization Modeling Complement Submodular Information Measures for Balanced and Robust Data Selection Consistent Identification of Top-$K$ Nodes in Noisy Networks Strichartz estimates for Schrödinger equations with the multipole Aharonov--Bohm Hamiltonian The Brunn-Minkowski inequality for the generalized Gaussian distribution Convergence and non-asymptotic error analysis for kinetic Langevin samplers using the exact harmonic Langevin integrator On the Sample Complexity of Robust Binary Hypothesis Testing The complexity of frugal digraph homomorphisms Associative Structures in Pseudo-Riemannian Lie Algebras On the Shirshov--Cohn theorem for JB-algebras Non-property (t) for SO(n,1) Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials On the asymptotics of ground states for a boundary value problem for the equation $-\varepsilon Δ_p u = a|u|^{q-2}u - b|u|^{γ-2}u$ Optimal Non-Asymptotic Edgeworth Expansions for Multivariate Neural Network Outputs From Halin's Edge Removability to Matching Removability in $k$-Connected Graphs Variational Contraction Conditions for Iterative Algorithms in Multi-Population Discrete-Time Regularized Mean-Field Games Fundamental Limitation in Explaining AI A magnetic eigenvalue bound in the disk Arakelov inequality for families of pairs Geometry of Neighborhoods of Minimal Rational Curves Betti numbers of inductively pierced codes Fibrations, the First Betti Number, and Almost Nonnegative Ricci Curvature On exotic rationally integrable planar dual billiards I. Complex geometry and type of dynamics Confidence intervals for causal effects in sequential decision making The $θ= \infty$ Conjecture and the Riemann Hypothesis for Automorphic $L$-functions Single-Chord Augmentation of Weighted Cycles for Algebraic Connectivity and Network Coherence On the fundamental spectral gap of weighted Schrodinger operators Incremental SVD for Large-Scale Dynamic Matrices: Accuracy, Subspace Stability, Refresh Strategies, and Financial Factor-Based Risk Models Matrix concentration inequalities for time-inhomogeneous Markov chains Random Neural Network Expressivity for Non-Linear Partial Differential Equations Lifted Schrödinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions A computational phase transition for learning-to-sample from Ising models Accuracy Analysis of the Proxy Point Method with Applications to Some Toeplitz Matrices Equivariant homotopy dense subsets in the realm of uniform G-ANR spaces Enumerating Pattern Avoiding Parking Functions Minimax Limits of k-Fold Cross-Validation via Majority Learning dynamical systems with biochemically informed neural ordinary differential equations Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance Odd Koschorke classes Embedding more than 8 symplectic balls in $\mathbb{C}\mathrm{P}^2$ Kernel Embedding for Operator-Valued Measures and Its Application to Quantum Tomography Framing Triangulations for Arbitrary Integer Flow Polytopes A Quasi Maximum Likelihood Estimation Method for Bergomi-Type Volatility Models Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux New inverse problems for a time-switched system of wave and diffusion equations Geometry-Preserving Nudged Elastic Band and Dimer Methods under Anisotropic Force Uncertainty Exponential mixing properties of nonlinear functional autoregressive models Designs, linear codes, plateaued functions, and their interconnections Comparison Geometry on Manifolds with Density via Modified Hessians Measuring multivariate maximal tail dependence AKLT State is Indeed the Observation Process of a causal Hidden quantum Markov Model On higher order Morrey's inequalities over RCD{\boldmath$(K,N)$}-spaces Spectral analysis and sine transform based preconditioning for a structure preserving stabilized scheme approximating the space-fractional Allen Cahn equation with logarithmic potential Optimal drift optimizer for non-convex optimization On Zappa-Szép products of two semidihedral groups Basic invariants for time-like surfaces in $\mathbb R^3_1$ with real asymptotic lines Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Beyond Algebraic Solutions to Stringy Spacetime Saturation for product systems of polynomials Orbit decomposition statistics for discrete dynamical systems: the Cesàro mean and a large deviation principle A dimension-free interpolation of Caffarelli's contraction theorem BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization Feature Learning in Wide Neural Networks under $μ$P: Identifiability and Sparse-Dictionary Decomposition of the Mean-Field Limit WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains Polynomial Context-Truncation Sensitivity in Autoregressive Language Models: Sequential Wyner-Ziv Bounds for KV Cache Compression IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization Deep ZakaiJ: Structured Filtering for Jump-Diffusion Time Series Forecasting From dual connections to gravitational field equations -- the curvature and Einstein tensors of the $α$ - connection of a quasi-statistical manifold Long Memory in Intrinsically Dynamic Factor Models Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signals Topological analysis in $\mathcal{R}(p,q)-$anisotropic sector and nuclear space on $\mathcal{R}(p,q)-$quantum deformed algebra On some arithmetic conditions of recurrent sequences modulo prime p Decoupling for AD-regular sets on the parabola Irremediably singular quantum branched covers Data-Specific Hyper-Parameter Design: A Paradigm Shift in Reservoir Computing The Normalized Maximum Likelihood for Regular Non-Smooth Models: Measure-Theoretic Foundations and Geometric Sampling Threshold-Safe Shock Absorption in a Compartmental Voter-Flow Model:\ A Conservative Impulse-Control Benchmark On the binary digits of the Erdős-Borwein constant Refined asymptotics of the steady Navier Stokes equation around small Landau solutions A Parameterized Algorithm for Testing whether the Limit of a Diagram is Empty Variational formulation of hyperbolic conservation laws On potentials of distributions in Orlicz-Hardy type spaces on the Heisenberg group Bayesian Conformal-Projective Prediction On Permutation Groups of Cyclic Codes over Finite Fields An Exact Continuous Conductance Formulation of the Hamiltonian Path Problem Crossing limit cycles of discontinuous piecewise differential systems with nilpotent saddles separated by a nonregular line Quantitative Stability of Generalized $p$-Area Minimizing Surfaces On the Differential-Geometric Equivalence of Hellinger-Kantorovich and Cone-Wasserstein Spaces On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs Boundary stabilization of an Euler-Bernoulli beam with axial force and internal delay The petrol station game: the regional average price. A mean field analysis On the Harris-Viehmann conjecture for Hodge-Newton reducible local Shimura data of abelian type On the complexity of extensions of non-archimedean Polish groups admitting a compatible complete left-invariant metric The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Hydrodynamic Limit of the Boltzmann Equation toward Generic Riemann Solutions with Shocks SinFormer: A Tailored Transformer for Robust Radio Frequency Fingerprint Identification Universality theorems for generalized splines
A Matrix Model for Higher-Genus Fuss--Catalan Numbers
Anatol Kiril · 2026-05-26 · via math updates on arXiv.org

View PDF HTML (experimental)

Abstract:The genus--g Fuss--Catalan (FC) number counts the number of ways to obtain a genus-g surface by identifying the edges of a pn--gon via p-valent hyperedges. For p=2 these are the genus--g Catalan numbers which are generated as the trace correlations in the Gaussian matrix model (GUE). Here we construct a simple two-matrix model which generates the higher-genus Fuss--Catalan numbers for any p as the coefficients of its 1/N-expansion. We obtain exact sum rules and an explicit formula for the higher-genus Fuss--Catalan numbers which generalises the Harer--Zagier formula to p>2. We discuss the relation of the higher-genus FC numbers to the intersection numbers and the Euler characteristic of the moduli space of spin-p curves.
Comments: 19 pages, 3 figures
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Cite as: arXiv:2605.24237 [hep-th]
  (or arXiv:2605.24237v1 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.2605.24237

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Ivan K. Kostov [view email]
[v1] Fri, 22 May 2026 21:29:31 UTC (347 KB)