Results 1 to 10 of about 1,690,008 (302)
A Unified Generalization of the Catalan, Fuss, and Fuss–Catalan Numbers
Mathematical and Computational Applications, 2019 In the paper, the authors introduce a unified generalization of the Catalan numbers, the Fuss numbers, the Fuss−Catalan numbers, and the Catalan−Qi function, and discover some properties of the unified generalization, including a product ...
Feng Qi, Xiao-Ting Shi, Pietro Cerone
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On a Family of Infinite Series with Reciprocal Catalan Numbers [PDF]
Axioms, 2022 We study a certain family of infinite series with reciprocal Catalan numbers. We first evaluate two special candidates of the family in closed form, where we also present some Catalan–Fibonacci relations.
Kunle Adegoke +2 more
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Noncommutative Catalan numbers [PDF]
Annals of Combinatorics, 2019 The goal of this paper is to introduce and study noncommutative Catalan numbers $C_n$ which belong to the free Laurent polynomial algebra in $n$ generators.
Berenstein, Arkady, Retakh, Vladimir
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s-Catalan numbers and Littlewood-Richardson polynomials [PDF]
Enumerative Combinatorics and Applications, 2022 : In this note, we study two generalizations of the Catalan numbers, namely the s -Catalan numbers and the spin s -Catalan numbers. These numbers first appeared in relation to quantum physics problems about spin multiplicities.
William Linz
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From entanglement witness to generalized Catalan numbers. [PDF]
Sci Rep, 2016 The problem of entanglement detection for arbitrary spin systems is analyzed. We demonstrate how a single measurement of the squared total spin can probabilistically discern separable from entangled many-particle states.
Cohen E, Hansen T, Itzhaki N.
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Positroid Catalan numbers [PDF]
Communications of the American Mathematical Society, 2021 Given a (bounded affine) permutation f f , we study the positroid Catalan number C f C_f defined to be the torus-equivariant Euler characteristic of the associated open positroid variety.
Pavel Galashin, T. Lam
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On a congruence involving $q$-Catalan numbers [PDF]
Comptes Rendus. Mathématique, 2020 Based on a $q$-congruence of the author and Petrov, we set up a $q$-analogue of Sun–Tauraso’s congruence for sums of Catalan numbers, which extends a $q$-congruence due to Tauraso.
Liu, Ji-Cai
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Generalized Catalan Numbers from Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2021 The Catalan numbers $C_{n} \in \{1,1,2,5,14,42,\dots \}$ form one of the most venerable sequences in combinatorics. They have many combinatorial interpretations, from counting bracketings of products in non-associative algebra to counting rooted plane ...
Paul E. Gunnells
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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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Convolution identities involving the central binomial coefficients and Catalan numbers [PDF]
Transactions on Combinatorics, 2021 We generalize some convolution identities due to Witula and Qi et al. involving the central binomial coefficients and Catalan numbers. Our formula allows us to establish many new identities involving these important quantities, and recovers some ...
Necdet Batır, Hakan Kucuk, Sezer Sorgun
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