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Catalan polynomials for the Wishart-Laguerre β-ensemble

  • Bei Kang
  • Lu-Yao Wang
  • Ke Wu
  • Wei-Zhong Zhao
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Abstract

By means of W-representation, we investigate the Wishart-Laguerre β-ensemble and present a compact expression for Catalan polynomials. For a special Nekrasov partition function associated with the Wishart-Laguerre β-ensemble, we show that it can be expressed as a exponential form of the special Catalan polynomials. Furthermore, we make a rule to calculate the Catalan polynomials by means of Feynman diagrams and present another expression for Catalan polynomials. We also establish the connection between certain Catalan polynomials and knot theory.

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Cite

BibTeXRIS
BibTeX
@misc{kang2026catalan,
  title = {{Catalan polynomials for the Wishart-Laguerre $β$-ensemble}},
  author = {Bei Kang and Lu-Yao Wang and Ke Wu and Wei-Zhong Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19634},
  eprint = {2610.19634},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19634},
}
RIS
TY  - UNPB
TI  - Catalan polynomials for the Wishart-Laguerre β-ensemble
AU  - Bei Kang
AU  - Lu-Yao Wang
AU  - Ke Wu
AU  - Wei-Zhong Zhao
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19634
UR  - https://arxiv.org/abs/2610.19634
AB  - By means of W-representation, we investigate the Wishart-Laguerre β-ensemble and present a compact expression for Catalan polynomials. For a special Nekrasov partition function associated with the Wishart-Laguerre β-ensemble, we show that it can be expressed as a exponential form of the special Catalan polynomials. Furthermore, we make a rule to calculate the Catalan polynomials by means of Feynman diagrams and present another expression for Catalan polynomials. We also establish the connection between certain Catalan polynomials and knot theory.
ER  -