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r-Whitney numbers of Dowling lattices
In this paper, we define the r -Whitney numbers of the first and second kind over Q n ( G ) , respectively. Expand
A note on the Bernoulli and Euler polynomials
  • Gi-Sang Cheon
  • Mathematics, Computer Science
  • Appl. Math. Lett.
  • 1 April 2003
In this paper, we obtain a simple property of the Bernoulli polynomials Bn(x) and En(x). Expand
Protected points in ordered trees
In this note we start by computing the average number of protected points in all ordered trees with n edges. Expand
Stirling matrix via Pascal matrix
Abstract The Pascal-type matrices obtained from the Stirling numbers of the first kind s(n,k) and of the second kind S(n,k) are studied, respectively. It is shown that these matrices can beExpand
An update on Minc's survey of open problems involving permanents
Abstract We summarise the progress which has been made since 1986 on the conjectures and open problems listed in H. Minc’s survey articles on the theory of permanents.
Combinatorics of Riordan arrays with identical A and Z sequences
We provide a combinatorial interpretation in terms of weighted Łukasiewicz paths and then look at several large classes of examples. Expand
Simple proofs of open problems about the structure of involutions in the Riordan group
Abstract We prove that if D = ( g ( x ) , f ( x ) ) is an element of order 2 in the Riordan group then g ( x ) = ± exp [ Φ ( x , xf ( x ) ] for some antisymmetric function Φ ( x , z ) . Also we proveExpand
Riordan group involutions and the Delta-sequence
An infinite lower triangular matrix D = (dn,k)n,k≥0 is called a Riordan matrix if its column k ≥ 0 has generating function g(z)(f (z))k. Expand
The elements of finite order in the Riordan group over the complex field
Abstract An element of finite order in the Riordan group over the real field must have order 1 or 2. If we extend all the entries to be complex numbers then it may have any finite order. In theExpand
Riordan group involutions
We study involutions in the Riordan group, especially those with combinatorial meaning. We give a new determinantal criterion for a matrix to be a Riordan involution and examine several classes ofExpand