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International Journal of Latest Research in Science and Technology

DOI:10.29111/ijlrst   ISRA Impact Factor:3.35

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Rightside-Left β-Numbers

Research Paper Open Access

International Journal of Latest Research in Science and Technology Vol.2 Issue 6, pp 124-127,Year 2013

RIGHTSIDE-LEFT β-NUMBERS

Ammar Seddiq Mahmood, Shukriyah Sabir Ali

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Received : 18 November 2013; Accepted : 25 November 2013 ; Published : 31 December 2013

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Abstract

For any partition μ = ( μ1, μ2, ..., μn ) of a non - negative integer number r there exist a diagram (A) of β - numbers for each e where e is a a positive integer number greater than or equal to two; which introduced by James in 1978.These diagrams (A) play an enormous role in Iwahori-Hecke algebras and q-Schur algebras; as presented by Fayers in 2007. In this paper we introduced a new diagram (A') by employing the "rightside-left " application on the main diagram (A). We concluded that we can find the successive main diagrams (A') for the guides b2, b3,. . . and be depending on the main diagram (A') for b1 and set this fact as a rule named Rule (3.1).We depended in our work on the idea of the intersection of the main diagrams (A) given by Mahmood in 2011 and the "upside-down β - numbers" again given by Mahmood in 2013.

Key Words   
β - numbers, Diagram (A), Intersection, Partition, Rightside- Left

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References
  1. Mathas, A. "Iwahori - Hecke Algebras and Schur Algebras of the Symmetric Groups", 1999, Amer. Math. Soc., University Lecture Series, 15.
  2. James, G., " Some combinatorial results involving Young diagrams", 1978, Math. Proc. Cambridge Philos. Soc., 83, 1-10.
  3. Fayers , M., "Another runner removal theorem for r-decomposition number of lwahori – Hecke algebras and q- Schur algebras", 2007, J. algebra, 310, 396 - 404.
  4. Mahmood, A. S., "On the intersection of Young's diagrams core", 2011, J. Education and Science (Mosul University), 24, no. 3, 143- 159.
  5. Mohammad, H. S., " Algorithms of The Core of Algebraic Young's Tableaux ", 2008 , M.Sc. Thesis, College of Education, University of Mosul.
  6. Mahmood, S. M., " On e - Regular and the Intersection of Young's Diagrams Core", 2011, M. Sc. Thesis, College of Education, University of Mosul.
  7. Mahmood, A. S., "Upside- down β- numbers", 2013, Australian J. of Basic and Applied Sciences 7, no. 7,986- 990.
To cite this article

Ammar Seddiq Mahmood, Shukriyah Sabir Ali , " Rightside-left β-numbers ", International Journal of Latest Research in Science and Technology . Vol. 2, Issue 6, pp 124-127 , 2013

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