A Rational Catalan Formula for (m, 3)-Hikita Polynomials

Catalan Numbers for Complex Reflection Groups

We construct (q, t)-Catalan polynomials and q-Fuss-Catalan polynomials for any irreducible complex reflection group W . The two main ingredients in this construction are Rouquier’s formulation of shift functors for the rational Cherednik algebras of W , and Opdam’s analysis of permutations of the irreducible representations of W arising from the Knizhnik-Zamolodchikov connection.

Some 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 ...

Generalization of a Formula of Touchard for Catalan Numbers

A method to obtain the best uniform polynomial approximation for the family of rational function

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

RIMS - 1824 Rigged Configurations and Catalan , Stretched Parabolic Kostka

We will look at the Catalan numbers from the Rigged Configurations point of view originated [9] from an combinatorial analysis of the Bethe Ansatz Equations associated with the higher spin anisotropic Heisenberg models . Our strategy is to take a combinatorial interpretation of Catalan numbers Cn as the number of standard Young tableaux of rectangular shape (n2), or equivalently, as the Kostka ...