Results 1 to 10 of about 1,655,826 (313)
A Unified Generalization of the Catalan, Fuss, and Fuss—Catalan Numbers [PDF]
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 ...
Xiao-Ting Shi, Feng Qi, Pietro Cerone
exaly +9 more sources
Some Properties of the Fuss–Catalan Numbers [PDF]
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
exaly +6 more sources
Three Identities of the Catalan-Qi Numbers [PDF]
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.
Feng Qi, Mansour Mahmoud
exaly +4 more sources
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
doaj +2 more sources
On weighted and bounded multidimensional Catalan numbers [PDF]
Enumerative Combinatorics and ApplicationsWe define a weighted analog for the multidimensional Catalan numbers, obtain matrix-based recurrences for some of them, and give conditions under which they are periodic.
Ryota Inagaki, Dimana Pramatarova
doaj +2 more sources
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
doaj +3 more sources
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
doaj +2 more sources
A Note on q-analogue of Degenerate Catalan Numbers Associated with p-adic Integral on Zp
Symmetry, 2022 In this paper, we introduce q-analogues of degenerate Catalan numbers and polynomials with the help of a fermionic p-adic q-integrals on Zp and establish some new connections with the degenerate Stirling numbers of the first and second kinds. Furthermore,
Waseem Ahmad Khan, Khan Waseem A
exaly +2 more sources
Some properties of the Catalan-Qi function related to the Catalan numbers. [PDF]
Springerplus, 2016 In the paper, the authors find some properties of the Catalan numbers, the Catalan function, and the Catalan-Qi function which is a generalization of the Catalan numbers. Concretely speaking, the authors present a new expression, asymptotic expansions, integral representations, logarithmic convexity, complete monotonicity, minimality, logarithmically ...
Qi F, Mahmoud M, Shi XT, Liu FF.
europepmc +4 more sources
Mathematics, 2023 In the paper, the authors briefly survey several generalizations of the Catalan numbers in combinatorial number theory, analytically generalize the Catalan numbers, establish an integral representation of the analytic generalization of the Catalan ...
Feng Qi, Wen-Hui Li, Jian Cao
exaly +3 more sources