Partial chord diagrams and matrix models

Abstract

In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length spectrum. Furthermore, we consider the boundary length and point spectrum that unifies the last two types of spectra. We introduce matrix models that encode generating functions of partial chord diagrams filtered by each of these spectra. Using these matrix models, we derive partial differential equations - obtained independently by cut-and-join arguments in an earlier work - for the corresponding generating functions.

42 pages, 14 figures

References in corpus (6)

• Generation of Matrix Models by W-operators
• Universality and asymptotics of graph counting problems in nonorientable surfaces
• Enumeration of linear chord diagrams
• Linear chord diagrams on two intervals
• Enumeration of chord diagrams via topological recursion and quantum curve techniques
• The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion

Cited by in corpus (2)

• Computing the spectral action for fuzzy geometries: from random noncommutative geometry to bi-tracial multimatrix models
• The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion