Results 21 to 30 of about 107,847 (314)
Some Properties of the Fuss–Catalan Numbers
Mathematics, 2018 In the paper, the authors express the Fuss⁻Catalan numbers as several forms in terms of the Catalan⁻Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the ...
Feng Qi, Pietro Cerone
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Holonomic equations and efficient random generation of binary trees [PDF]
Discrete Mathematics & Theoretical Computer ScienceHolonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. Rémy showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary trees.
Pierre Lescanne
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$m$-noncrossing partitions and $m$-clusters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $W$ be a finite crystallographic reflection group, with root system $\Phi$. Associated to $W$ there is a positive integer, the generalized Catalan number, which counts the clusters in the associated cluster algebra, the noncrossing partitions for $W$,
Aslak Bakke Buan +2 more
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Several explicit and recursive formulas for generalized Motzkin numbers
AIMS Mathematics, 2020 In the paper, the authors find two explicit formulas and recover a recursive formula for generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the ...
Feng Qi, Bai-Ni Guo
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New Expressions for Sums of Products of the Catalan Numbers
Axioms, 2021 In this paper, we perform a further investigation for the Catalan numbers. By making use of the method of derivatives and some properties of the Bell polynomials, we establish two new expressions for sums of products of arbitrary number of the Catalan ...
Conghui Xie, Yuan He
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IDEAS AND PROJECTS IN THE FIELD OF ARCHITECTURE AND URBANISM FROM THE MATERIALS OF THE CATALAN PERIODICALS OF THE SECOND REPUBLIC [PDF]
Латиноамериканский исторический альманах, 2021 Catalan architects who were members of the G.A.T.C.P.A.C. associa-tion and the Association of Architects of Catalonia (SAC) were con-cerned about social, demographic and sanitary issues.
Nataliya Kuzina
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Arithmetic of weighted Catalan numbers [PDF]
Journal of Number Theory, 2021 27 ...
Yibo Gao, Andrew Gu
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Journal of Mathematical Analysis and Applications, 2009 AbstractBy combining inverse series relations with binomial convolutions and telescoping method, moments of Catalan numbers are evaluated, which resolves a problem recently proposed by Gutiérrez et al. [J.M. Gutiérrez, M.A. Hernández, P.J. Miana, N. Romero, New identities in the Catalan triangle, J. Math. Anal. Appl. 341 (1) (2008) 52–61].
CHEN X., CHU, Wenchang
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On the Euler function of the Catalan numbers [PDF]
Journal of Number Theory, 2012 AbstractWe study the solutions of the equation ϕ(Cm)/ϕ(Cn)=r, where r is a fixed rational number, Ck is the kth Catalan number and ϕ is the Euler function. We note that the number r=4 is special for this problem and for it we construct solutions (m,n) to the above equation which are related to primes p such that 2p−1 or 4p−3 is also prime.
Luca, Florian, Stănică, Pantelimon
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