Results 41 to 50 of about 107,847 (314)

The Problem of Separatism in Modern Spain: the Catalan Question

Проблемы постсоветского пространства, 2022
Catalan nationalism, rooted in the 19th century, transformed into separatism in the 1980s, threatening the existence of the Spanish state. The unstable political situation in the country caused by the crisis of the party system and serious economic ...
S. M. Gavrilova
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Cores with distinct parts and bigraded Fibonacci numbers

, 2017
The notion of $(a,b)$-cores is closely related to rational $(a,b)$ Dyck paths due to Anderson's bijection, and thus the number of $(a,a+1)$-cores is given by the Catalan number $C_a$.
Paramonov, Kirill
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On generalised catalan numbers

Discrete Mathematics, 1978
AbstractThe Catalan number Cn is defined to be 2nn(n+1). One of its occurrences is as the number of ways of bracketing a product of n+1 terms taken from a set with binary operation. In this note the corresponding result for a set with a k-ary operation is considered.
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On a new congruence in the Catalan triangle [PDF]

Notes on Number Theory and Discrete Mathematics
For 0≤k≤n, the number C(n,k) represents the number of all lattice paths in the plane from the point (0,0) to the point (n,k), using steps (1,0) and (0,1), that never rise above the main diagonal y = x.
Jovan Mikić
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Catalan numbers revisited

Journal of Mathematical Analysis and Applications, 1985
Motivated by author's earlier development of binomial functions [ibid. 70, 460-473 (1979; Zbl 0416.05007); ibid. 83, 110-125 (1981; Zbl 0477.05004)] the notion of Catalan binomial functions, Catalan matrices and that of Sheffer functions is introduced as a generalization of the same named sequences.
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Moments of combinatorial and Catalan numbers

Journal of Number Theory, 2010
In this paper we obtain the moments {m}m0 defined by. where (mn) is the usual combinatorial number. We also provide the moments in the Catalan triangle whose (n,p) entry is defined by. and, in particular, new identities involving the well-known Catalan numbers. © 2010 Elsevier Inc.
Miana, P.J., Romero, N.
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Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials)

, 2017
Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain ...
Proctor, Robert A., Willis, Matthew J.
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Catalan numbers, q-Catalan numbers and hypergeometric series

Journal of Combinatorial Theory, Series A, 1987
The author derives a new \(q\)-analog of the Catalan numbers: \[ {\mathcal C}_ n(\lambda,q)=q^{2n}\prod \frac{1+\lambda q^{2i-3}}{1-q^{2i}},\quad 1\leq i\leq n. \] The usual Catalan numbers are given by \({\mathcal C}_ n={\mathcal C}_ n(-1,1)\). In addition to this representation as a rational function in \(q\), Andrews' \(q\)-Catalan numbers have a ...
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Ears of triangulations and Catalan numbers

Discrete Mathematics, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferran Hurtado, Marc Noy
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Generalized compositions with a fixed number of parts [PDF]

, 2010
We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of the Catalan ...
Janjic, Milan
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