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CANONICAL CHARACTERS ON QUASI-SYMMETRIC FUNCTIONS AND BIVARIATE CATALAN NUMBERS
Hopf algebra character quasi-symmetric function central binomial coefficient
2015/8/14
Every character on a graded connected Hopf algebra decomposes uniquely as
a product of an even character and an odd character [2]. We obtain explicit formulas for
the even and odd parts of the unive...
This article proves a conjecture by S.-C. Liu and C.-C. Yeh about Catalan numbers, which states that odd Catalan numbers can take exactly k − 1 distinct values modulo 2k, namely the values C21 &...
Generalized catalan numbers, sequences and polynomials
Generalized catalan numbers sequences polynomials
2010/12/20
In this paper we present an algebraic interpretation for generalized Catalan numbers. We describe them as dimensions of certain subspaces of multilinear polynomials. This description is of utmost impo...
We define a new sequence of positive integers, associated with Catalan numbers and Narayana polynomials.
The Limiting Distribution of the Coefficients of the q-Catalan Numbers
Bernoulli number q-Catalan number unimodality log-concavity moment generating function
2014/6/3
We show that the limiting distributions of the coefficients of the q-Catalan numbers and the generalized q-Catalan numbers are normal. Despite the fact that these coefficients are not unimodal for sma...