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Discrete Mathematics, ISSN 0012-365X, 07/2019, Volume 342, Issue 7, pp. 2139 - 2147
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+r is positive definite. We study the family of... 
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
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 8/2010, Volume 32, Issue 1, pp. 67 - 97
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
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
Electronic Journal of Combinatorics, ISSN 1077-8926, 2011, Volume 18, Issue 1
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
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
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
Journal of Algebraic Combinatorics, ISSN 0925-9899, 12/2012, Volume 36, Issue 4, pp. 649 - 673
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
... > 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
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
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
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
Journal Article
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