Results 11 to 20 of about 18,619 (166)
Results in Nonlinear Analysis, 2021 In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing the ratio of two central binomial coefficients which are related to the ...
Feng Qi, Chao-Ping Chen , Dongkyu Lim
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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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Factors of alternating convolution of the Gessel numbers [PDF]
Notes on Number Theory and Discrete MathematicsThe Gessel number P(n,r) is the number of lattice paths in the plane with (1,0) and (0,1) steps from (0,0) to (n+r, n+r-1) that never touch any of the points from the set {(x,x)∈ℤ²:x≥r}. We show that there is a close relationship between Gessel numbers P(
Jovan Mikić
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Symmetry of Narayana Numbers and Rowvacuation of Root Posets
Forum of Mathematics, Sigma, 2021 For a Weyl group W of rank r, the W-Catalan number is the number of antichains of the poset of positive roots, and the W-Narayana numbers refine the W-Catalan number by keeping track of the cardinalities of these antichains.
Colin Defant, Sam Hopkins
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Three Identities of the Catalan-Qi Numbers
Mathematics, 2016 In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternative proofs of two identities of the Catalan numbers. The three identities of the Catalan-Qi numbers generalize three identities of the Catalan numbers.
Mansour Mahmoud, Feng Qi
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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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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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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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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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