Hankel Transform of (q,r)-Dowling Numbers

The Hankel transform

The Dowling Transform of Subspace Arrangements

We define the Dowling transform of a real frame arrangement and show how the characteristic polynomial changes under this transformation. As a special case, the Dowling transform sends the braid arrangement An to the Dowling arrangement. Using Zaslavsky's characterization of supersolvability of signed graphs, we show supersolvability of an arrangement is preserved under the Dowling transform. W...

The Translated Dowling Polynomials and Numbers

More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated D...

Transformations Preserving the Hankel Transform

Transformations Preserving the Hankel Transform Christopher French Department of Mathematics and Statistics Grinnell College Grinnell, IA 50112 USA [email protected] Abstract We classify all polynomial transformations of integer sequences which preserve the Hankel transform, thus generalizing examples due to Layman and Spivey & Steil. We also show that such transformations form a group ...

The Hankel Transform of the Sum of Consecutive Generalized Catalan Numbers

X iv :m at h/ 06 04 42 2v 1 [ m at h. C O ] 1 9 A pr 2 00 6 The Hankel Transform of the Sum of Consecutive Generalized Catalan Numbers Predrag Rajković, Marko D. Petković, University of Nǐs, Serbia and Montenegro Paul Barry School of Science, Waterford Institute of Technology, Ireland Abstract. We discuss the properties of the Hankel transformation of a sequence whose elements are the sums of c...