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Science China Mathematics, ISSN 1674-7283, 5/2019, Volume 62, Issue 5, pp. 999 - 1028
In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply twelve... 
11B83 | 05A40 | degenerate Bernoulli polynomial | Krobov polynomial of the first kind | 05A19 | Mathematics | generalized Pascal functional matrix | Applications of Mathematics | Wronskian matrix | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
2009, ISBN 9780195334548, xiv, 422
Like the intriguing Fibonacci and Lucas numbers, Catalan numbers are also ubiquitous. "They have the same delightful propensity for popping up unexpectedly,... 
Catalan numbers (Mathematics) | Mathematics | Euler's triangulation problem | Pascal's triangle | Pascal's identity | Lucas numbers | Catalan sequence | Parenthesization problem | Catalan numbers | Martin gardner | Fibonacci numbers
Book
Linear Algebra and Its Applications, ISSN 0024-3795, 03/2014, Volume 444, pp. 114 - 131
In this paper we establish plenty of number theoretic and combinatoric identities involving generalized Bernoulli polynomials and Stirling numbers of both... 
Bernoulli matrix | Bernoulli polynomials | Pascal matrix | Stirling numbers | Hyperharmonic numbers | Stirling matrix | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | DEGENERATE BERNOULLI | LINEAR ALGEBRA | Mathematics - Number Theory
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2008, Volume 308, Issue 18, pp. 4246 - 4262
We consider an identity relating Fibonacci numbers to Pascal's triangle discovered by G.E. Andrews. Several authors provided proofs of this identity, most of... 
Hypergeometric functions | Pascal's triangle | Identity of Andrews | Riordan array | Catalan's triangle | MATHEMATICS | hypergeometric functions | CATALAN NUMBERS | identity of Andrews | INVERSION | FORMULA | FIBONACCI NUMBERS | SUMS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2008, Volume 156, Issue 14, pp. 2793 - 2803
In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices,... 
Generalized Fibonacci numbers | Combinatorial identities | Iteration matrix | Fibonacci numbers | Bell polynomials | POLYNOMIALS | MATHEMATICS, APPLIED | LINEAR ALGEBRA | GENERALIZED PASCAL MATRIX | STIRLING MATRIX
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 2014, Volume 64, Issue 2, pp. 287 - 300
Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal's triangle. We... 
combinatorial properties | Pascal triangles | linear recurrences | POLYNOMIALS | MATHEMATICS | CHEBYSHEV | MORGAN-VOYCE | SUMS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 08/2012, Volume 312, Issue 15, pp. 2197 - 2202
We obtain explicit formulas that express the complete homogeneous symmetric polynomials of the sequence of partial sums sk of a sequence xk as polynomials in... 
Legendre–Stirling numbers | Symmetric polynomials | Gaussian coefficients | Generalized Stirling numbers | [formula omitted]-Stirling numbers | q-Stirling numbers | Legendre-Stirling numbers | MATHEMATICS | DIVIDED DIFFERENCES | PASCAL MATRICES
Journal Article
Indian Journal of Pure and Applied Mathematics, ISSN 0019-5588, 10/2007, Volume 38, Issue 5, pp. 457 - 465
In this paper, the Lucas matrix L-n is introduced. Let P-n[x] and Q(n)[x] be the generalized Pascal matrix of first and second kinds, which are defined in... 
Pascal matrix | Combinatorial identity | Lucas matrix | Factorization of matrix | MATHEMATICS | factorization of matrix | combinatorial identity
Journal Article
International Journal of Heat and Mass Transfer, ISSN 0017-9310, 01/2016, Volume 92, pp. 1034 - 1040
•A new meshless approach to tackle different inverse heat source problems accurately.•The novel scheme is applicable for inverse heat source problems with 10-1... 
Adjoint Trefftz test functions | Green’s second identity | Reciprocity gap functional | Heat source recovery problem | Pascal polynomials | Green's second identity | CAUCHY-PROBLEM | IDENTIFICATION | ENGINEERING, MECHANICAL | NUMERICAL-SOLUTION | MECHANICS | CONDUCTION EQUATION | THERMODYNAMICS | TEMPERATURE | FUNDAMENTAL-SOLUTIONS
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 07/2019, Volume 778, pp. 73 - 77
A bound resembling Pascal's identity is presented for binary necklaces with fixed density using Lyndon words with fixed density. The result is generalized to... 
Necklaces | Lyndon word | Pascal's identity | Nichols algebras | Fixed-density | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 4/2014, Volume 64, Issue 2, pp. 287 - 300
Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We... 
Algebra | linear recurrences | Mathematics, general | Mathematics | Primary 11B39, 05A19, 11A55, 05A10, 11B65, 05A15 | combinatorial properties | Pascal triangles
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2019, Volume 16, Issue 5, pp. 1 - 20
In this contribution, some new identities involving Sheffer–Appell polynomial sequences using generalized Pascal functional and Wronskian matrices are deduced.... 
33C45 | identities | 15A24 | generalized Pascal functional | Mathematics, general | Mathematics | Wronskian matrices | 15A15 | Sheffer–Appell polynomial sequence | orthogonal polynomials | MATHEMATICS | DETERMINANTAL APPROACH | MATHEMATICS, APPLIED | APOSTOL-BERNOULLI | Sheffer-Appell polynomial sequence
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2003, Volume 130, Issue 3, pp. 527 - 534
The Pascal matrix and the Stirling matrices of the first kind and the second kind obtained from the Fibonacci matrix are studied, respectively. Also, we obtain... 
Fibonacci matrix | Pascal matrix | Stirling matrix of the first kind | Stirling matrix of the second kind | MATHEMATICS, APPLIED | MATRICES
Journal Article
Organon F, ISSN 1335-0668, 2018, Volume 25, Issue 2, pp. 196 - 214
In this paper, I try to argue that, from the methodological position of reflected equilibrium, it seems to be reasonable to build a theory of personal identity... 
Epistemology | Philosophy of Science | Marya Schechtman | Reflected equilibrium | Afterlife | Pascal's wager | Life | Personal identity | Radim Belohrad | Samuel Scheffler | Person | IDENTITY | reflected equilibrium | afterlife | PHILOSOPHY | person-life | personal identity | Scheffler
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 02/2015, Volume 253, pp. 83 - 101
A simple but elegant method was adopted in Youn and Yang (2011) in order to derive a differential equation and recursive formulas for Sheffer polynomials.... 
Generalized Pascal functional matrix | Umbral calculus | Wronskian matrix | Sheffer sequences | MATHEMATICS, APPLIED | NUMBERS
Journal Article
ACAROLOGIA, ISSN 0044-586X, 2019, Volume 59, Issue 2, pp. 261 - 278
The identity of Blaise Pascal's mite is examined. Linguistics, morphology, habitat and size reveal that Pascal's mite is not Acarus siro L., as usually... 
Blaise Pascal | SCABIES | MEDICINE | CHEESE | Sarcoptes scabiei (L.) | Acarus siro L | ENTOMOLOGY | mite | ciron
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2017, Volume 446, Issue 1, pp. 87 - 100
This paper deals with a unified matrix representation for the Sheffer polynomials. The core of the proposed approach is the so-called creation matrix, a... 
Binomial type polynomials | Generalized Pascal matrix | Sheffer polynomials | Appell polynomials | Creation matrix | MATHEMATICS | DETERMINANTAL APPROACH | MATHEMATICS, APPLIED | BELL POLYNOMIALS | SEQUENCES | IDENTITIES
Journal Article
Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 10/2016, Volume 22, Issue 2, pp. 329 - 335
Graph lattice has vertices at points with non-negative integer coordinates. From each vertex we have two edges: horizontal and vertical neighboring vertices... 
Pascal’s triangle | Combinatorial identity | Random walks | The probability of transition | 05C63 Infinite graphs | Mathematics, general | Mathematics | Directed graph | Reachability of vertices | 05C81 Random walks on graphs | Pascal's triangle
Journal Article
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