Discrete Mathematics, ISSN 0012-365X, 07/2019, Volume 342, Issue 7, pp. 2139 - 2147

The Catalan number sequence is one of the most famous number sequences in combinatorics and is well studied in the literature...

Catalan number sequence | Stieltjes determinate sequences | Bernstein functions | Fuss–Catalan number sequence | Stieltjes moment sequences | Double factorial number sequence | MATHEMATICS | HAUSDORFF | DENSITIES | Fuss-Catalan number sequence | Mathematics - Combinatorics

Catalan number sequence | Stieltjes determinate sequences | Bernstein functions | Fuss–Catalan number sequence | Stieltjes moment sequences | Double factorial number sequence | MATHEMATICS | HAUSDORFF | DENSITIES | Fuss-Catalan number sequence | Mathematics - Combinatorics

Journal Article

Mathematics (Basel), ISSN 2227-7390, 2018, Volume 6, Issue 12, p. 277

In the paper, the authors express the Fuss–Catalan numbers as several forms in terms of the Catalan...

Logarithmic convexity | Fuss-Catalan number | Catalan-Qi function | Catalan number | Minimality | Complete monotonicity | Monotonicity | Inequality | GAMMA | Catalan-Qi-function | INEQUALITIES | REPRESENTATION | RATIO | monotonicity | complete monotonicity | logarithmic convexity | MATHEMATICS | inequality | VALUES | minimality | Fuss–Catalan number | Catalan–Qi function

Logarithmic convexity | Fuss-Catalan number | Catalan-Qi function | Catalan number | Minimality | Complete monotonicity | Monotonicity | Inequality | GAMMA | Catalan-Qi-function | INEQUALITIES | REPRESENTATION | RATIO | monotonicity | complete monotonicity | logarithmic convexity | MATHEMATICS | inequality | VALUES | minimality | Fuss–Catalan number | Catalan–Qi function

Journal Article

DOCUMENTA MATHEMATICA, ISSN 1431-0643, 2010, Volume 15, pp. 939 - 955

We prove that if p, r is an element of R, p >= 1 and 0 <= r <= p then the Fuss-Catalan sequence (mp+r m) r/mp+r is positive definite. We study the family of...

MATHEMATICS | Fuss-Catalan numbers | free | boolean and monotonic convolution | CONVOLUTION

MATHEMATICS | Fuss-Catalan numbers | free | boolean and monotonic convolution | CONVOLUTION

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2011, Volume 139, Issue 10, pp. 3735 - 3738

In this paper we give explicitly a family of probability densities, the moments of which are Fuss-Catalan numbers...

Numbers | Mathematical moments | Matrices | Mathematics | Mathematical theorems | Density | Fuss-catalan numbers | Free Bessel laws | Moments | MATHEMATICS | MATHEMATICS, APPLIED | moments | Fuss-Catalan numbers | free Bessel laws | MATRICES

Numbers | Mathematical moments | Matrices | Mathematics | Mathematical theorems | Density | Fuss-catalan numbers | Free Bessel laws | Moments | MATHEMATICS | MATHEMATICS, APPLIED | moments | Fuss-Catalan numbers | free Bessel laws | MATRICES

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 8/2010, Volume 32, Issue 1, pp. 67 - 97

In type A, the q,t-Fuß–Catalan numbers can be defined as the bigraded Hilbert series of a module associated to the symmetric group...

Mathematics | Cherednik algebra | Nonnesting partition | Fuß–Catalan number | q , t -Catalan number | Shi arrangement | Convex and Discrete Geometry | Catalan number | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Dyck path | Computer Science, general | Combinatorics | Fuß-Catalan number | Q,t-Catalan number

Mathematics | Cherednik algebra | Nonnesting partition | Fuß–Catalan number | q , t -Catalan number | Shi arrangement | Convex and Discrete Geometry | Catalan number | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Dyck path | Computer Science, general | Combinatorics | Fuß-Catalan number | Q,t-Catalan number

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 9/2017, Volume 30, Issue 3, pp. 1170 - 1190

We consider Gaussian elliptic random matrices X of a size $$N \times N$$ N × N with parameter $$\rho $$ ρ , i.e., matrices whose pairs of entries $$(X_{ij},...

15B52 | Random matrices | Elliptic law | Narayana numbers | Singular values | Type B | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Fuss–Catalan numbers | 60F05 | RANEY DISTRIBUTIONS | PROBABILITY | Fuss-Catalan numbers | DENSITIES | PRODUCTS | STATISTICS & PROBABILITY | POWERS | Resveratrol

15B52 | Random matrices | Elliptic law | Narayana numbers | Singular values | Type B | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Fuss–Catalan numbers | 60F05 | RANEY DISTRIBUTIONS | PROBABILITY | Fuss-Catalan numbers | DENSITIES | PRODUCTS | STATISTICS & PROBABILITY | POWERS | Resveratrol

Journal Article

Colloquium Mathematicum, ISSN 0010-1354, 2012, Volume 129, Issue 2, pp. 189 - 202

We describe the class of probability measures whose moments are given in terms of the Aval numbers...

Fuss-catalan numbers | Multiplicative free convolution | Raney sequence | MATHEMATICS | multiplicative free convolution | Fuss-Catalan numbers

Fuss-catalan numbers | Multiplicative free convolution | Raney sequence | MATHEMATICS | multiplicative free convolution | Fuss-Catalan numbers

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 2011, Volume 18, Issue 1

.... These complexes are used to refine Catalan numbers and Fuss-Catalan numbers, by introducing colour statistics for triangulations and Fuss-Catalan complexes...

Schlegel diagram | Triangulation | Fuß-catalan complex | Lagrange-good inversion formula | Simplicial complex | Catalan number | Barycentric subdivision | Fuß-catalan number | Vertex colouring | MATHEMATICS | triangulation | MATHEMATICS, APPLIED | Fuss-Catalan complex | Fuss-Catalan number | vertex colouring | simplicial complex | Lagrange-Good inversion formula | FORMULAS | barycentric subdivision

Schlegel diagram | Triangulation | Fuß-catalan complex | Lagrange-good inversion formula | Simplicial complex | Catalan number | Barycentric subdivision | Fuß-catalan number | Vertex colouring | MATHEMATICS | triangulation | MATHEMATICS, APPLIED | Fuss-Catalan complex | Fuss-Catalan number | vertex colouring | simplicial complex | Lagrange-Good inversion formula | FORMULAS | barycentric subdivision

Journal Article

Journal of Computational Analysis and Applications, ISSN 1521-1398, 06/2019, Volume 26, Issue 6, pp. 1047 - 1058

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2016, Volume 368, Issue 12, pp. 8499 - 8518

...]. Also we provide a simple analytic proof that for any real p and r with p>0, the Fuss-Catalan or Raney numbers \frac {r}{pn+r}\binom {pn+r}{n}, n=0,1...

Completely monotone sequence | Random matrices | Fuss-Catalan numbers | Complete Bernstein function | Canonical sequence | Concave distribution function | Infinitely divisible | Exchangeable trials | complete Bernstein function | MATHEMATICS | concave distribution function | random matrices | DENSITIES | exchangeable trials | canonical sequence | infinitely divisible

Completely monotone sequence | Random matrices | Fuss-Catalan numbers | Complete Bernstein function | Canonical sequence | Concave distribution function | Infinitely divisible | Exchangeable trials | complete Bernstein function | MATHEMATICS | concave distribution function | random matrices | DENSITIES | exchangeable trials | canonical sequence | infinitely divisible

Journal Article

11.
Full Text
Fuss–Catalan matrices, their weighted sums, and stabilizer subgroups of the Riordan group

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2017, Volume 532, pp. 25 - 42

In this paper, we present the Riordan arrays called Fuss–Catalan matrices which are constructed by the convolutions of the generating functions of the Fuss–Catalan numbers...

Fundamental theorem of Riordan arrays | Generating function | Stabilizer | Fuss–Catalan matrices | Catalan numbers | Fuss–Catalan numbers | Riordan group | Fuss-Catalan matrices | MATHEMATICS, APPLIED | Fuss-Catalan numbers | NUMBERS | IDENTITIES | SEQUENCES | ENUMERATION | ARRAYS | MATHEMATICS | TRIANGLES | PARTITIONS | COMBINATORICS

Fundamental theorem of Riordan arrays | Generating function | Stabilizer | Fuss–Catalan matrices | Catalan numbers | Fuss–Catalan numbers | Riordan group | Fuss-Catalan matrices | MATHEMATICS, APPLIED | Fuss-Catalan numbers | NUMBERS | IDENTITIES | SEQUENCES | ENUMERATION | ARRAYS | MATHEMATICS | TRIANGLES | PARTITIONS | COMBINATORICS

Journal Article

Journal of Integer Sequences, 01/2018, Volume 21, Issue 2

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 12/2018, Volume 558, pp. 25 - 43

We study generalized Catalan matrices based on the Riordan array and Fuss–Catalan numbers. A unified combinatorial interpretation for the entries of the generalized Catalan matrices is presented by means of m-Dyck paths...

Generalized binomial series | m-Dyck path | Fuss–Catalan number | Generating function | Riordan array | Generalized Catalan matrix | MATHEMATICS, APPLIED | NUMBERS | IDENTITIES | SEQUENCES | POWER | MATHEMATICS | Fuss-Catalan number | TRIANGLES

Generalized binomial series | m-Dyck path | Fuss–Catalan number | Generating function | Riordan array | Generalized Catalan matrix | MATHEMATICS, APPLIED | NUMBERS | IDENTITIES | SEQUENCES | POWER | MATHEMATICS | Fuss-Catalan number | TRIANGLES

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 12/2012, Volume 36, Issue 4, pp. 649 - 673

.... A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in $\operatorname{NC}(W...

Noncrossing partition lattice | Coxeter element | Complex reflection group | Lyashko–Looijenga covering | Fuß–Catalan number | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Combinatorics | Computer Science, general | Finite Coxeter group | Fuß-Catalan number | Lyashko-Looijenga covering | MATHEMATICS | NON-CROSSING PARTITIONS | Fu beta-Catalan number

Noncrossing partition lattice | Coxeter element | Complex reflection group | Lyashko–Looijenga covering | Fuß–Catalan number | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Combinatorics | Computer Science, general | Finite Coxeter group | Fuß-Catalan number | Lyashko-Looijenga covering | MATHEMATICS | NON-CROSSING PARTITIONS | Fu beta-Catalan number

Journal Article

Advances in Applied Mathematics, ISSN 0196-8858, 03/2014, Volume 54, Issue 1, pp. 11 - 26

We study a circular order on labelled, m-edge-coloured trees with k vertices, and show that the set of such trees with a fixed circular order is in bijection...

Fuss–Catalan number | Enumeration | Tree of relations | Labelled triangulation | Induction | RNA secondary structure | Tree | Edge-coloured | m-Angulation | RNA m-diagram | Polygon | Interval exchange transformation | Fuss-Catalan number | MATHEMATICS, APPLIED | CATALAN | RNA

Fuss–Catalan number | Enumeration | Tree of relations | Labelled triangulation | Induction | RNA secondary structure | Tree | Edge-coloured | m-Angulation | RNA m-diagram | Polygon | Interval exchange transformation | Fuss-Catalan number | MATHEMATICS, APPLIED | CATALAN | RNA

Journal Article

Documenta Mathematica, ISSN 1431-0635, 2013, Volume 18, Issue 2013, pp. 1573 - 1596

... > 1 is a rational number and 0 < r <= p then mu(p, r) is absolutely continuous and its density W-p,W-r(x...

Meijer G-function | Free convolution | Generalized hypergeometric function | Mellin convolution | MATHEMATICS | PROBABILITY | generalized hypergeometric function | free convolution | FUSS-CATALAN NUMBERS | RANDOM MATRICES

Meijer G-function | Free convolution | Generalized hypergeometric function | Mellin convolution | MATHEMATICS | PROBABILITY | generalized hypergeometric function | free convolution | FUSS-CATALAN NUMBERS | RANDOM MATRICES

Journal Article

Lithuanian Mathematical Journal, ISSN 0363-1672, 04/2010, Volume 50, Issue 2, pp. 121 - 132

Let x be a complex random variable such that Ex = 0, E|x|(2) = 1, and E|x|(4) < infinity. Let x(ij), i, j is an element of {1, 2,...}, be independent copies of...

Random matrices | Fuss-Catalan numbers | Semi-circular law | Marchenko-Pastur distribution | MATHEMATICS | semi-circular law | random matrices | Universities and colleges

Random matrices | Fuss-Catalan numbers | Semi-circular law | Marchenko-Pastur distribution | MATHEMATICS | semi-circular law | random matrices | Universities and colleges

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 10/2018, Volume 17, Issue 10

We examine m-cluster theory from an elementary point of view using a generalization of m + 1-ary trees which we call m-noncrossing trees. We show that these...

quivers | exceptional sequences | c -vectors | m -cluster category | mutation of m -clusters | Fuss-Catalan numbers | MATHEMATICS | MATHEMATICS, APPLIED | c-vectors | STABILITY CONDITIONS | CLUSTER ALGEBRAS | TRIANGULATED CATEGORIES | COMBINATORICS | m-cluster category | mutation of m-clusters

quivers | exceptional sequences | c -vectors | m -cluster category | mutation of m -clusters | Fuss-Catalan numbers | MATHEMATICS | MATHEMATICS, APPLIED | c-vectors | STABILITY CONDITIONS | CLUSTER ALGEBRAS | TRIANGULATED CATEGORIES | COMBINATORICS | m-cluster category | mutation of m-clusters

Journal Article

Mathematical and computational applications, 05/2019, Volume 24, Issue 2, p. 49

In the paper, the authors introduce a unified generalization of the Catalan numbers, the Fuss numbers, the Fuss...

Fuss–Catalan number | Fuss number | product-ratio expression | logarithmically complete monotonicity of the second order | Catalan number | Catalan–Qi function | unified generalization | integral representation

Fuss–Catalan number | Fuss number | product-ratio expression | logarithmically complete monotonicity of the second order | Catalan number | Catalan–Qi function | unified generalization | integral representation

Journal Article

05/2018, ISBN 9781119414346, 33

The Catalan numbers, the generalized Catalan numbers, the Fuss numbers, and the Fuss...

Fuss–Catalan–Qi function | Fuss–Catalan number | Fuss number | generalization | Catalan number | property | generating function | Catalan–Qi function | Fuss-Catalan number | Generating function | Catalan-Qi function | Fuss-Catalan-Qi function | Generalization | Property

Fuss–Catalan–Qi function | Fuss–Catalan number | Fuss number | generalization | Catalan number | property | generating function | Catalan–Qi function | Fuss-Catalan number | Generating function | Catalan-Qi function | Fuss-Catalan-Qi function | Generalization | Property

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