Multivariate Fuss-Catalan numbers and B-quasisymmetric functions
نویسنده
چکیده
We study the ideal generated by constant-term free B-quasisymmetric polynomials, and prove that the quotient of the polynomial ring by this ideal has dimension given by 1 2n+1 ` 3n
منابع مشابه
Some Properties of the Fuss–catalan Numbers
In the paper, the authors express the Fuss–Catalan numbers as several forms in terms of the Catalan–Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the Fuss–Catalan numbers, and derive a double inequality for bounding the Fuss–Catalan numbers.
متن کاملCanonical Characters on Quasi-Symmetric Functions and Bivariate Catalan Numbers
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 universal character on the Hopf algebra of quasi-symmetric functions. They can be described in terms of Legendre’s beta function evaluated at halfintegers, or in terms of bivariate Catalan numbers: C(m, n...
متن کاملMultivariate Fuss-Catalan numbers
are integers that appear in many combinatorial problems. These numbers first arose in the work of Catalan as the number of triangulations of a polygon by mean of nonintersecting diagonals. Stanley [13, 14] maintains a dynamic list of exercises related to Catalan numbers, including (at this date) 127 combinatorial interpretations. Closely related to Catalan numbers are ballot numbers. Their name...
متن کاملProduct of Ginibre matrices: Fuss-Catalan and Raney distributions.
Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions P(s)(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions P(s)(x) in terms of a combination of s hypergeometric functions of the type (s)F(s-1). The explicit formula derived here...
متن کاملParking Functions and Vertex Operators
We introduce several associative algebras and series of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we a series of representations of symmetric groups which turn out to be isomorphic to parking function modules. We also construct series of vector spaces whose dimensions are Catalan number...
متن کامل