A Note on Random Matrix Integrals, Moment Identities, and Catalan Numbers
نویسندگان
چکیده
We relate Catalan numbers and Catalan determinants to random matrix integrals and to moments of spin representations of odd orthogonal groups. §
منابع مشابه
9 M ay 2 00 8 IDENTITIES INVOLVING NARAYANA POLYNOMIALS AND CATALAN NUMBERS
Abstract. We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the Narayana polynomials by three different identities. We give three different proofs for these identities, namely, two algebraic proofs and one combinatorial proof. Some applications are also given which lead t...
متن کاملA Note on the Strong Law of Large Numbers
Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...
متن کاملSome New Binomial Sums Related to the Catalan Triangle
In this paper, we derive many new identities on the classical Catalan triangle C = (Cn,k)n>k>0, where Cn,k = k+1 n+1 ( 2n−k n ) are the well-known ballot numbers. The first three types are based on the determinant and the fourth is relied on the permanent of a square matrix. It not only produces many known and new identities involving Catalan numbers, but also provides a new viewpoint on combin...
متن کاملCurious Relations and Identities Involving the Catalan Generating Function and Numbers
Riordan matrix methods and manipulation of various generating functions are used to find curious relations among the Catalan, central binomial, and RNA generating functions. In addition, the Wilf-Zeilberger method is used to find identities where the gamma function and Catalan numbers are expressed in terms of the Gauss hypergeometric function. As a consequence of the identities, new recurrence...
متن کاملSome Identities and a Matrix Inverse Related to the Chebyshev Polynomials of the Second Kind and the Catalan Numbers
In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer powers and higher order derivatives of the generating function of the Chebyshev polynomials of the second kind respectively, find an explicit formula and an identity for the Chebyshev polynomials ...
متن کامل