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CANONICAL CHARACTERS ON QUASI-SYMMETRIC FUNCTIONS AND BIVARIATE CATALAN NUMBERS
Hopf algebra character quasi-symmetric function central binomial coefficient
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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...
The odd Catalan numbers modulo 2^k
odd Catalan numbers modulo 2^k
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2011/1/19
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
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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...
Catalan numbers and a new integer sequence
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2010/12/9
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
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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...