African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 254

Article in Press

On The Polygonal And Circular Representations Of The (123) – Avoiding Petterns Of Aunu Permutations

Chun P.b, Choji NM, Ajai PT, Adidi CS

  •  Received: 15 April 2020
  •  Accepted: 12 May 2020
In this communication, another theoretic Property of the (123)- Avoiding class of AUNU permutation patterns is x-rayed. Here, we consider the Polygonal and Circular representations as studied by Paulus Gerdes of these patterns with a view of exploring more of their pictorial applications in relation to interconnection Networks e.t.c. These algebraic structures had found wide applications in almost all facets of applied mathematics such as Association/Succession schemes, Thin cyclic design, Latin squares, Lattices, Automate theory, Graph theory, Coding theory e.t.c. Our results are obtained by the consideration of the Cayley tables of these patterns used by Ibrahim and Abubakar to study their Non-associativity/non-commutativity. The methods here is considering the rows of these Cayley tables as the (123)-avoiding AUNU permutation patterns. Our goal is achieved by considering these Patterns for where n is prime. The polygonal and circular Representation of these patterns are thus obtained with the aim of giving some graphical network structures. It is also seen that the polygonal and circular representation of the (123)-avoiding AUNU Patterns has resulted to very interesting symmetrical designs/figures/shapes which could fit in some special purposeful interconnections or network designs or some special classes of Graphs. In particular, the Polygonal Representation of (13524), (14253) and (15432) Fig (g) gives rise to a beautiful shape of a kite. This Paper has exposed yet another important application of the (123)- avoiding patterns of the AUNU permutations.

Keywords: AUNU Permutation Patterns, Cayley Tables, Polygonal Representation, Circular Representation, Non-associative/non-commutativity Property.