Results 11 to 20 of about 63,525 (216)

Special Numbers and Polynomials Including Their Generating Functions in Umbral Analysis Methods

Axioms, 2018
In this paper, by applying umbral calculus methods to generating functions for the combinatorial numbers and the Apostol type polynomials and numbers of order k, we derive some identities and relations including the combinatorial numbers, the Apostol ...
Yilmaz Simsek
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Weighted Tree-Numbers of Matroid Complexes [PDF]

Discrete Mathematics & Theoretical Computer Science, 2015
We give a new formula for the weighted high-dimensional tree-numbers of matroid complexes. This formula is derived from our result that the spectra of the weighted combinatorial Laplacians of matroid complexes consist of polynomials in the weights.
Woong Kook, Kang-Ju Lee
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Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials

Mathematics, 2022
In this paper, we study limit theorems for numbers satisfying a class of triangular arrays, which are defined by a bivariate linear recurrence with bivariate linear coefficients.
Igoris Belovas
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Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function

Axioms, 2019
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new ...
Irem Kucukoglu, Burcin Simsek, Yilmaz Simsek   +2 more
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Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series

Journal of Inequalities and Applications, 2019
The main purpose and motivation of this work is to investigate and provide some new identities, inequalities and relations for combinatorial numbers and polynomials, and for Peters type polynomials with the help of their generating functions. The results
Yilmaz Simsek, Ji Suk So
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Tribonacci graphs [PDF]

ITM Web of Conferences, 2020
Special numbers have very important mathematical properties alongside their numerous applications in many fields of science. Probably the most important of those is the Fibonacci numbers.
Demirci Musa, Cangul Ismail Naci
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The Combinatorial Fusion Cascade to Generate the Standard Genetic Code

Life, 2021
Combinatorial fusion cascade was proposed as a transition stage between prebiotic chemistry and early forms of life. The combinatorial fusion cascade consists of three stages: eight initial complimentary pairs of amino acids, four protocodes, and the ...
Alexander Nesterov-Mueller, Roman Popov
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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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Several identities containing central binomial coefficients and derived from series expansions of powers of the arcsine function

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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A Brief Survey and an Analytic Generalization of the Catalan Numbers and Their Integral Representations

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 ...
Jian Cao, Wen-Hui Li, Da-Wei Niu, Feng Qi, Jiao-Lian Zhao   +4 more
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