Research output: Working paper › Research

**Partial chord diagrams and matrix models.** / Andersen, Jørgen Ellegaard; Fuji, Hiroyuki; Manabe, Masahide ; Penner, Robert C.; Sulkowski, Piotr.

Research output: Working paper › Research

Andersen, JE, Fuji, H, Manabe, M, Penner, RC & Sulkowski, P 2016 'Partial chord diagrams and matrix models' arXiv.org.

Andersen, J. E., Fuji, H., Manabe, M., Penner, R. C., & Sulkowski, P. (2016). *Partial chord diagrams and matrix models*. arXiv.org.

Andersen JE, Fuji H, Manabe M, Penner RC, Sulkowski P. 2016. Partial chord diagrams and matrix models. arXiv.org.

Andersen, Jørgen Ellegaard et al. *Partial chord diagrams and matrix models*. arXiv.org. 2016., 42 p.

Andersen JE, Fuji H, Manabe M, Penner RC, Sulkowski P. Partial chord diagrams and matrix models. arXiv.org. 2016 Dec 17.

Andersen, Jørgen Ellegaard ; Fuji, Hiroyuki ; Manabe, Masahide ; Penner, Robert C. ; Sulkowski, Piotr. / **Partial chord diagrams and matrix models**. arXiv.org, 2016.

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title = "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.",

author = "Andersen, {J{\o}rgen Ellegaard} and Hiroyuki Fuji and Masahide Manabe and Penner, {Robert C.} and Piotr Sulkowski",

year = "2016",

month = "12",

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language = "English",

publisher = "arXiv.org",

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AU - Andersen, Jørgen Ellegaard

AU - Fuji, Hiroyuki

AU - Manabe, Masahide

AU - Penner, Robert C.

AU - Sulkowski, Piotr

PY - 2016/12/17

Y1 - 2016/12/17

N2 - 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.

AB - 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.

M3 - Working paper

BT - Partial chord diagrams and matrix models

PB - arXiv.org

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