## Search

Now showing items 11-18 of 18

JavaScript is disabled for your browser. Some features of this site may not work without it.

All of UDORACommunitiesTitleAuthorsIssue DateSubmit DateSubjectsThis CollectionTitleAuthorsIssue DateSubmit DateSubjects

Subjects

Applied mathematics (18)

Discrete mathematics (18)Proceedings (1)Pure mathematics (1)View MoreJournalBulletin of the Institute of Combinatorics and its Applications (ICA) (7)Fibonacci Quarterly (6)Utilitas Mathematica (3)Carpathian Journal of Mathematics (1)Electronic Notes in Discrete Mathematics (1)AuthorsBagdasar, Ovidiu (2)01f9023f-d29d-4a5e-9798-89f4c5851ab9 (1)81a26182-8169-4390-b85f-b5fad16813cb (1)a90cc4fe-8caf-4587-ab1d-ca6360cecf5b (1)afaa2e14-da18-425a-9673-04ed98ca29b9 (1)View MoreYear (Issue Date)2014-05 (4)2016-08 (2)2014 (1)2014-02 (1)2015 (1)View MoreTypesArticle (18)
AboutResearcher Submission of Outputs to REF2021University NewsTools for ResearchersLibraryUDoTake down policy

Now showing items 11-18 of 18

- List view
- Grid view
- Sort Options:
- Relevance
- Title Asc
- Title Desc
- Issue Date Asc
- Issue Date Desc
- Results Per Page:
- 5
- 10
- 20
- 40
- 60
- 80
- 100

On cyclicity and density of some Catalan polynomial sequences

Larcombe, Peter J.; Fennessey, Eric J. (The Institute of Combinatorics and its Applications, 2014-05)

We give proofs of cyclic and density properties of some sequences generated by Catalan polynomials, and other observations.

A polynomial based construction of periodic Horadam sequences

Larcombe, Peter J.; Fennessey, Eric J. (The Institute of Combinatorics and its Applications (ICA), 2016-03)

A recent matrix based approach to the study of self-repeating Horadam sequences has identified a mechanism to produce guaranteed (and arbitrary) periodicity through a novel formulation for the two governing parameters in the defining linear Horadam recurrence equation. We consider this further here, giving supporting examples to illustrate the methodology which utilises so called Catalan polynomials.

Some factorisation and divisibility properties of Catalan polynomials

Jarvis, Frazer A.; Larcombe, Peter J.; Fennessey, Eric J. (The Institute of Combinatorics and its Applications, 2014-05)

We present some factorisation and divisibility properties of Catalan polynomials. Initial results established with ad hoc proofs then make way for a more systematic approach and use of the well developed theory of cyclotomic polynomials.

On the evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations using a hypergeometric approach

Larcombe, Peter J. (The Fibonacci Association, 2016-08)

Infinite series comprising exponentiated multiples of p-term linear combinations of Catalan numbers arise naturally from a related power series expansion for sin(2pα) (in odd powers of sin(α)) which itself has an interesting history. In this article some explicit results generated previously by the author (for p = 1, 2, 3) are discussed in the context of this general problem of series summation, and new evaluations made for the cases p = 4, 5 by way of further examples. A powerful hypergeometric approach is adopted which offers, from the analytical formulation developed, a means to achieve these particular evaluations and in principle many others for even greater values of p.

A condition for anti-diagonals product invariance across powers of $2 \times 2$ matrix sets characterizing a particular class of polynomial families

Larcombe, Peter J.; Fennessey, Eric J. (The Fibonacci Association, 2015-05)

Motivated by some recent work on a particular class of polynomial families associated with certain types of integer sequences, we formulate a sufficient condition under which the anti-diagonals products across sets of characterizing 2 × 2 matrices remain invariant as matrix power increases. Two proofs are given along with some examples.

On the structure of periodic complex Horadam orbits

Bagdasar, Ovidiu; Larcombe, Peter J.; Anjum, Ashiq (North University of Baia Mare (Romania), 2016-01-16)

Numerous geometric patterns identified in nature, art or science can be generated from recurrent sequences, such as for example certain fractals or Fermat’s spiral. Fibonacci numbers in particular have been used to design search techniques, pseudo random-number generators and data structures. Complex Horadam sequences are a natural extension of Fibonacci sequence to complex numbers, involving four parameters (two initial values and two in the defining recursion), therefore successive sequence terms can be visualized in the complex plane. Here, a classification of the periodic orbits is proposed, based on divisibility relations between orders of generators (roots of the characteristic polynomial). Regular star polygons, bipartite graphs and multisymmetric patterns can be recovered for selected parameter values. Some applications are also suggested.

The Asymptotic Form of the Sum $\sum_{i=0}^{n} i^{p} { n+i \choose i }$: Two Proofs

Larcombe, Peter J.; Kirschenhofer, Peter; Fennessey, Eric J. (The Institute of Combinatorics and its Applications, 2014)

The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.