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

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

The class of generating functions for completely monotone sequences (moments of finite positive measures on [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

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

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

... A. Similar trees are in bijection with complete exceptional sequences. Most of this paper is expository, explaining definitions and known results about these topics in representation theory...

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

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

6.
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, 2018, Volume 21, Issue 6

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 4/2017, Volume 27, Issue 2, pp. 379 - 424

We study coagulation–fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of...

Detailed balance | Convergence to equilibrium | 37L15 | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | 35Q99 | Mathematics | Fish schools | Complete monotonicity | 70F45 | 44A10 | Analysis | Appl.Mathematics/Computational Methods of Engineering | Fuss–Catalan sequences | Bernstein functions | 45J05 | 92D50 | MATHEMATICS, APPLIED | LAW | EQUATIONS | LIMIT | PHYSICS, MATHEMATICAL | ASYMPTOTIC-BEHAVIOR | BALANCE | Fuss-Catalan sequences | DISTRIBUTIONS | MECHANICS | EQUILIBRIUM | DYNAMICS | CONVERGENCE | Schools | Statistics | Dynamical Systems

Detailed balance | Convergence to equilibrium | 37L15 | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | 35Q99 | Mathematics | Fish schools | Complete monotonicity | 70F45 | 44A10 | Analysis | Appl.Mathematics/Computational Methods of Engineering | Fuss–Catalan sequences | Bernstein functions | 45J05 | 92D50 | MATHEMATICS, APPLIED | LAW | EQUATIONS | LIMIT | PHYSICS, MATHEMATICAL | ASYMPTOTIC-BEHAVIOR | BALANCE | Fuss-Catalan sequences | DISTRIBUTIONS | MECHANICS | EQUILIBRIUM | DYNAMICS | CONVERGENCE | Schools | Statistics | Dynamical Systems

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...

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

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

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

We prove that if p >= 1 and 0 < r <= p then the sequence ((mp+r)(m)) r/mp+r is positive definite...

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

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

Journal Article

Journal of Integer Sequences, 12/2015, Volume 19, Issue 1

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 07/2015, Volume 92, Issue 1, p. 012121

We investigate the level density for several ensembles of positive random matrices of a Wishart-like structure, W = XX dagger, where X stands for a...

RANEY DISTRIBUTIONS | PROBABILITY | SINGLE RING THEOREM | PHYSICS, FLUIDS & PLASMAS | PHASE-TRANSITION | SINGULAR-VALUES | POWERS | PHYSICS, MATHEMATICAL | FUSS-CATALAN NUMBERS

RANEY DISTRIBUTIONS | PROBABILITY | SINGLE RING THEOREM | PHYSICS, FLUIDS & PLASMAS | PHASE-TRANSITION | SINGULAR-VALUES | POWERS | PHYSICS, MATHEMATICAL | FUSS-CATALAN NUMBERS

Journal Article

05/2018, ISBN 9781119414346, 33

...–Catalan numbers are integer sequences, which have a long history, are of combinatorial interpretations, and have been attracting combinatorialists and number theorists...

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

Book Chapter

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

01/2014

...}$. Among the many generalizations of this sequence, the Fuss-Catalan numbers $C^{(d)}_k$ count enumerations of dissections of polygons $P_{k(d-1)+2}$ into $(d+1)$-gons...

Mathematics - Combinatorics

Mathematics - Combinatorics

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

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