Hostname: page-component-89b8bd64d-5bvrz Total loading time: 0 Render date: 2026-05-07T01:10:14.249Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOTE ON RANDOM MATRIX INTEGRALS, MOMENT IDENTITIES, AND CATALAN NUMBERS

Part of: Combinatorics Compact groups

Published online by Cambridge University Press:  06 May 2016

Nicholas M. Katz
Nicholas M. Katz*
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, U.S.A. email nmk@math.princeton.edu
Get access

Abstract

We relate Catalan numbers and Catalan determinants to random matrix integrals and to moments of spin representations of odd orthogonal groups.

MSC classification

Primary: 22C05: Compact groups
Secondary: 05A19: Combinatorial identities, bijective combinatorics

Information

Type
Research Article
Information
Mathematika , Volume 62 , Issue 3 , 2016 , pp. 811 - 817
Copyright
Copyright © University College London 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Gessel, I. and Viennot, X., Determinants, paths, and plane partitions. Preprint, 1989, http://www.cs.brandeis.edu/∼ira.Google Scholar
Katz, N. M. and Sarnak, P. C., Random Matrices, Frobenius Eigenvalues, and Monodromy (American Mathematical Society Colloquium Publications 45 ), American Mathematical Society (Providence, RI, 1999).Google Scholar
Keating, J. P. and Snaith, N. C., Random matrix theory and L-functions at s = 1/2. Comm. Math. Phys. 214(1) 2000, 57–89.Google Scholar
Kedlaya, K. and Sutherland, A., Hyperelliptic curves, L-polynomials, and random matrices. In Arithmetic, Geometry, Cryptography and Coding Theory (Contemporary Mathematics 487 ), American Mathematical Society (Providence, RI, 2009), 119–162.Google Scholar
Krattenthaler, C., Determinants of (generalised) Catalan numbers. J. Statist. Plann. Inference 140(8) 2010, 2260–2270.CrossRefGoogle Scholar
Shapiro, L., A short proof of an identity of Touchard’s concerning Catalan numbers. J. Combin. Theory Ser. A 20 1976, 375–376.Google Scholar
Sloane, N., The On-line Encyclopedia of Integer Sequences, https://oeis.org/.Google Scholar
Stanley, R., Catalan Numbers, Cambridge University Press (New York, 2015).Google Scholar
Touchard, J., Sur certaines équations fontionnelles. In Proceedings of the International Mathematical Congress (Toronto, 1924), Vol. 1, University of Toronto Press (1928), 465–472.Google Scholar
Varadarajan, V. S., Supersymmetry for Mathematicians: an Introduction (Courant Lecture Notes in Mathematics 11 ), New York University, Courant Institute of Mathematical Sciences (New York, 2004) American Mathematical Society, Providence, RI.Google Scholar
Weyl, H., Classical Groups, Princeton University Press (Princeton, NJ, 1946).Google Scholar