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Discrete Mathematics, ISSN 0012-365X, 07/2019, Volume 342, Issue 7, pp. 2139 - 2147
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2016, Volume 368, Issue 12, pp. 8499 - 8518
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
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
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
Journal Article
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
Journal Article
Mathematics (Basel), ISSN 2227-7390, 2018, Volume 6, Issue 12, p. 277
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
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
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
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
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
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
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 8/2010, Volume 32, Issue 1, pp. 67 - 97
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
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
Journal Article
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