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Applied Mathematics and Computation, ISSN 0096-3003, 04/2014, Volume 232, pp. 132 - 143
Journal Article
Discrete Mathematics, ISSN 0012-365X, 07/2015, Volume 338, Issue 7, pp. 1067 - 1074
We derive a combinatorial equilibrium for bounded juggling patterns with a random, q-geometric throw distribution. The dynamics are analyzed via rook... 
Markov process | Combinatorial stationary distribution | Ferrers board | [formula omitted]-Stirling number | Juggling pattern | q-Stirling number | POLYNOMIALS | MATHEMATICS | Q-STIRLING NUMBERS | SEQUENCES
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 04/2016, Volume 27, Issue 4, pp. 259 - 267
The asymptotic behaviour of the Chebyshev-Stirling numbers of the second kind, a special case of the Jacobi-Stirling numbers, has been established in a recent... 
Chebyshev-Stirling numbers | Riemann zeta function | 05E05 | 11B75 | Jacobi-Stirling numbers | Asymptotics | 05A16 | Chebyshev–Stirling numbers | Jacobi–Stirling numbers | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | NORMALITY | FORMULA | Probability | Chebyshev approximation | Paper | Integrals | Asymptotic properties | Transforms | Images
Journal Article
Discrete Mathematics, ISSN 0012-365X, 08/2012, Volume 312, Issue 15, pp. 2337 - 2348
Let G be a finite group of order m≥1. A Dowling lattice Qn(G) is the geometric lattice of rank n over G. In this paper, we define the r-Whitney numbers of the... 
Lah numbers | Whitney numbers | Dowling lattice | [formula omitted]-Stirling numbers | Dowling polynomials | Riordan group | r-Stirling numbers | MATHEMATICS | RIORDAN ARRAYS | Statistics | Questions and answers
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
Indagationes Mathematicae, ISSN 0019-3577, 03/2019, Volume 30, Issue 2, pp. 365 - 374
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 2009, Volume 116, Issue 3, pp. 539 - 563
Journal Article
Indagationes Mathematicae, ISSN 0019-3577, 01/2016, Volume 27, Issue 1, pp. 100 - 111
We define q-poly-Bernoulli polynomials Bn,ρ,q(k)(z) with a parameter ρ, q-poly-Cauchy polynomials of the first kind cn,ρ,q(k)(z) and of the second kind... 
[formula omitted]-poly-Bernoulli polynomials | Jackson’s integrals | Bernoulli numbers | [formula omitted]-poly-Cauchy polynomials | Cauchy numbers | Weighted Stirling numbers
Journal Article
Discrete Mathematics, ISSN 0012-365X, 10/2013, Volume 313, Issue 20, pp. 2127 - 2138
Stirling numbers and Bessel numbers have a long history, and both have been generalized in a variety of directions. Here, we present a second level... 
Partitions | [formula omitted]-Permutations | Telephone exchange | Riordan matrices | Stirling numbers | Bessel numbers | Semi-bipartite | G-Permutations | MATHEMATICS | Frames | Joining | Inverse | Mathematical analysis | Combinatorial analysis | Preserves
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 02/2019, Volume 255, pp. 222 - 233
T. A. Dowling introduced Whitney numbers of the first and second kinds concerning the so-called Dowling lattices of finite groups. It turned out that they are... 
[formula omitted]-Whitney–Lah numbers | [formula omitted]-Whitney numbers | r-Whitney numbers | r-Whitney–Lah numbers | MATHEMATICS, APPLIED | CONCAVITY | r-Whitney-Lah numbers | Lattices | Combinatorial analysis
Journal Article
International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, 02/2017, Volume 48, Issue 2, pp. 267 - 277
In this note, we revisit the problem of polynomial interpolation and explicitly construct two polynomials in n of degree k + 1, P k (n) and Q k (n), such that... 
Eulerian numbers | recurrence relation | sums of powers of integers | D-numbers | Stirling numbers of the second kind | Polynomial interpolation | Numbers | Algebra | Mathematical Formulas | Mathematics Instruction | Equations (Mathematics) | Geometric Concepts | Mathematics Education | Mathematics
Journal Article
2012, ISBN 9780123852182
This chapter elaborates the definitions and notations of some special functions, polynomials, and numbers. The special functions include the gamma, beta, the... 
Euler polynomials and numbers | Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials | Multiple Gamma functions | Asymptotic expansion for [formula omitted] | Generalized Euler polynomials and numbers | Asymptotic formula for the Gamma function | Gamma function | Euler-Mascheroni constant γ | Generalized (or Hurwitz) Zeta function [formula omitted] | Chu-Vandermonde theorem | Tchebycheff polynomials of the first and second kind | Gegenbauer (or ultraspherical) polynomials | p-adic L-functions | Generalized harmonic numbers of order [formula omitted] | Glaisher-Kinkelin constant A | Inequalities for the Gamma function and the double Gamma function | Bohr-Mollerup theorem | Jacobi polynomials | Bernoulli polynomials and numbers | Gauss hypergeometric function | Generalizations and unified presentations of the Apostol type polynomials | Kummer's expression for [formula omitted] | Pochhammer symbol [formula omitted] | Chu-Vandermonde summation formula | Struve functions | Generalized Bernoulli polynomials and numbers | Mellin-Barnes contour integral representation | Gauss's formulas for [formula omitted] | Legendre functions of the first and second kind | Euler-Maclaurin summation formula | Polygamma functions | Psi (or Digamma) function | Complete Elliptic integrals of the first and second kind | Harmonic numbers [formula omitted] | Error function [formula omitted] (probability integral) | Determinants of the Laplacians | Residue Calculus | Triple Gamma function | p-adic analytic extension | Generating functions | Whittaker function of the first kind | Stirling's formula for n! and its generalizations | Incomplete Beta functions | Series associated with the Zeta and related functions | Legendre's duplication formula and Gauss's multiplication formula for the Gamma function | Beta function | Hermite polynomials | Stirling numbers of the first and second kind | Double Gamma function | Laguerre functions and polynomials | Dufresnoy-Pisot theorem | Bessel functions | Lommel functions | Confluent hypergeometric function | Logarithmic convexity | n-ple Hurwitz Zeta functions | Generalized (Gauss and Kummer) hypergeometric function [formula omitted] | Poisson–Charlier polynomials | Incomplete Gamma function | Genocchi polynomials and numbers
Book Chapter
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 2013, Volume 36, Issue 2, pp. 465 - 479
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 2007, Volume 38, Issue 2, pp. 258 - 266
We present two extensions of the linear bound, due to Marcus and Tardos, on the number of 1-entries in an n × n ( 0 , 1 ) -matrix avoiding a fixed permutation... 
Stanley–Wilf conjecture | Ordered hypergraph | [formula omitted]-Matrix | Extremal theory | Stanley-Wilf conjecture | (0, 1)-Matrix | extremal theory | MATHEMATICS, APPLIED | (0.1)-matrix | MATRICES | ordered hypergraph | PARTITIONS
Journal Article
AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 04/2016, Volume 13, Issue 1, pp. 38 - 53
A k-ranking of a directed graph G is a labeling of the vertex set of G with k positive integers such that every directed path connecting two vertices with the... 
Directed path | Adjacency matrix | K-ranking | Directed cycle | Sierpinski triangle | k-ranking
Journal Article
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