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3, 1)
(10, 10, 10, 9,
9, 8, 8, 6, 5, 5,
5, 3, 1)
(11, 10, 8, 6,
6, 6, 5, 3, 3,
2, 2, 1, 1, 1)
(11, 11, 10, 8,
8, 4, 3, 3, 2, 2,
2, 1, 1, 1)
B
(11, 11, 11,
10, 8, 6, 6, 6,
5, 3, 1, 1, 1)
(11, 11, 9, 9,
9, 8, 6, 6, 5, 4,
3, 3, 2)
(11, 11, 11, 9,
8, 8, 7, 7, 4, 3,
2, 2, 1)
(11, 11, 11, 9,
8, 8, 7, 7, 4,
3, 2, 2, 1 )
(11, 11, 9, 9,
9, 8, 6, 6, 5, 4,
3, 3, 2)
C
(13, 13, 13,
12, 9, 5, 5, 2,
1, 1, 1)
(13, 13, 11,
11, 9, 4, 2, 2,
1, 1, 1)
(13, 13, 13
,11, 9, 4, 2, 2,
1, 1, 1)
(13, 13, 13,
11, 9, 4, 2, 2,
1, 1, 1)
(13, 13, 11,
11, 9, 4, 2, 2,
1, 1, 1)
D
(12, 12, 12,
11, 9, 8, 6, 5,
3, 1, 1, 1)
(12, 12, 12,
11, 11, 9, 6, 5,
4, 3, 3, 2)
(12, 12, 12,
11, 11, 9, 8, 4,
3, 2, 2, 1)
(12, 12, 12,
11, 11, 9, 8,
4, 3, 2, 2, 1)
(12, 12, 12,
11, 11, 9, 6, 5,
4, 3, 3, 2)
E
(12, 12, 12,
12, 8, 6, 6, 6,
2, 1, 1, 1, 1)
(12, 11, 9, 8,
7, 7, 6, 6, 5, 4,
3, 3, 2)
(12, 12, 11, 9,
8, 6, 6, 5, 4, 3,
2, 2, 1)
(12, 12, 11, 9,
8, 6, 6, 5, 4,
3, 2, 2, 1)
(12, 11, 9, 8,
7, 7, 6, 6, 5, 4,
3, 3, 2)
F
(12, 8, 6, 6,
6, 2, 1, 1, 1,
1)
(15, 14, 12,
11, 10, 8, 8, 5,
3, 2)
(15, 15, 14,
12, 11, 9, 9, 6,
3, 1)
(9, 8, 6, 6, 5,
4, 3, 2, 2, 1)
(8, 7, 7, 6, 6,
5, 4, 3, 3, 2)
G
(11, 11, 11,
10, 7, 7, 7, 7,
(10, 10, 9, 9,
9, 8, 6, 4, 2, 2,
(11, 10, 9, 9,
8, 8, 6, 4, 2, 2,
(11, 11, 11,
10, 10, 9, 6,
(11, 11, 11,
10, 9, 8, 6, 4,
6, 2, 1, 1, 1)
1, 1, 1)
1, 1, 1)
4, 2, 2, 1, 1,
1)
2, 2, 1, 1, 1)
H
(13, 11, 10,
8, 7, 7, 7, 7,
6, 4, 3, 1)
(13, 13, 12,
10, 10, 9, 9, 8,
8, 5, 3, 2)
(13, 12, 10,
10, 9, 9, 8, 8,
7, 6, 3, 1)
(13, 12, 10,
10, 9, 9, 8, 8,
6, 3, 1)
(13, 13, 12,
10, 10, 9, 9, 8,
8, 5, 3, 2)
I
(15, 15, 15,
12, 8, 4, 1, 1,
1)
(14, 12, 10,
10, 8, 6, 6, 4,
2)
(15, 14, 12,
12, 8, 4, 4, 2,
1)
(15, 14, 12,
12, 8, 4, 4, 2,
1)
(14, 12, 10,
10, 8, 6, 6, 4,
2)
J
(14, 11, 10,
8, 4, 1 ,1 ,1)
(15, 13, 11,
11, 9, 6, 1, 1)
(16, 15, 13,
13, 9, 5, 1, 1)
(11, 11, 7, 5,
4, 4, 2, 1)
(9, 9, 7, 5, 5,
4, 4, 2)
K
(15, 13, 11,
10, 7, 7, 5, 4,
3, 1)
(15, 12, 8, 8,
8, 8, 8, 5, 3, 2)
(15, 12, 11, 7,
7, 7, 7, 6, 3, 1)
(15, 12, 11, 7,
7, 7, 7, 6, 3,
1)
(15, 12, 8, 8,
8, 8, 8, 5, 3, 2)
L
(17, 17, 17,
17, 13, 9, 5,
1)
(8, 8, 6, 5, 4,
3, 3, 2)
(11, 7, 5,4, 3,
2, 2, 1)
(17, 17, 16,
14, 10, 6, 3,
1)
(17, 16, 14,
11, 8, 5, 3, 2)
M
(12, 9, 9, 8,
7, 7, 6, 5, 5,
4, 3, 2, 1)
(11, 11, 11, 9,
8, 8, 8, 7, 4, 3,
1)
(11, 11, 9, 9,
9, 8, 6, 5, 5, 4,
3, 1)
(12, 11, 9, 8,
7, 7, 6, 4, 3,
3, 3, 1, 1)
(12, 12, 11, 9,
8, 5, 4, 4, 4, 3,
1, 1, 1)
N
(11, 9, 8, 8,
7, 6, 6, 6, 6,
5, 4, 4, 3, 1)
(11, 11, 10, 8,
8, 8, 8, 8, 8, 8,
8, 5, 3, 2)
(11, 10, 8, 8,
8, 8, 8, 7, 7, 7,
7, 6, 3, 1)
(11, 10, 9, 9,
8, 8, 7, 7, 6,
3, 1)
(11, 11, 10,
10, 9, 9, 8, 8,
7, 7, 5, 5, 3, 2)
O
(12, 12, 12,
11, 8, 8, 5, 5,
2, 1, 1, 1)
(12, 12, 12,
11, 11, 9, 4, 2,
2, 1, 1, 1)
(12, 12, 12,
11, 11, 9, 4, 2,
2, 1, 1, 1)
(12, 12, 12,
11, 11, 9, 4,
2, 2, 1, 1, 1)
(12, 12, 12,
11, 11, 9, 4, 2,
2, 1, 1, 1)
P
(11, 11, 11,
8, 6, 6, 6, 5,
3, 1, 1, 1)
(12, 12, 10, 9,
8, 6, 6, 3, 2, 2,
1)
(12, 12, 12,
10, 9, 7, 7, 4,
1, 1)
(10, 8, 7, 7, 7,
7, 7, 4, 3, 2,
2, 1)
(8, 8, 8, 7, 5,
5, 5, 5, 4, 3, 3,
2)
Q
(11, 11, 11,
11, 10, 10, 8,
8, 5, 5, 2, 1,
1, 1)
(10, 10, 10, 9,
9, 7, 7, 7, 4, 2,
2, 1, 1, 1)
(10, 10, 10, 9,
9, 7, 4, 4, 4, 2,
2, 1, 1, 1)
(11, 11, 11,
11, 11, 11,
11, 9, 4, 2, 2,
1, 1, 1)
(11, 11, 11,
11, 11, 11, 11,
9, 4, 2, 2, 1, 1,
1)
R
(13, 11, 10,
8, 6, 6, 6, 5,
3, 1, 1, 1)
(12, 12, 10,
10, 10, 9, 9, 8,
8, 5, 3, 2)
(12, 12, 12,
10, 9, 9, 8, 8,
7, 6, 3, 1)
(13, 12, 9, 8,
8, 7, 7, 4, 3,
2, 2, 1)
(13, 13, 9, 9,
8, 6, 6, 5, 4, 3,
3, 2)
S
(13, 13, 13,
12, 7, 7, 2, 1,
1, 1)
(13, 11, 8, 7,
7, 3, 3, 3, 1)
(14, 13, 11, 6,
6, 5, 5, 1)
(12, 12, 11, 8,
7, 4, 3, 1, 1,
1)
(11, 11, 8, 6,
5, 5, 4, 3, 1, 1)
T
(14, 10, 6, 2,
1, 1, 1, 1, 1)
(16, 15, 13,
11, 11, 9, 6, 5,
5)
(16, 16, 15,
13, 13, 9, 7, 6,
3)
(13, 10, 6, 5,
3, 3, 1, 1, 1)
(11, 9, 8, 7, 5,
5, 3, 1, 1)
U
(14, 14, 12,
(15, 15, 14,
(15, 14, 12,
(14, 14, 14,
(14, 14, 14,
10, 9, 7, 6, 4,
3, 1)
12, 10, 7, 6, 5,
4, 4)
12, 10, 9, 5, 4,
3, 3)
13, 10, 9, 7,
6, 3, 1)
13, 13, 10, 8,
5, 3, 2)
V
(16, 13, 12,
11, 8, 8, 5)
(17, 16, 9, 3,
3, 3, 3)
(16, 14, 7, 6,
3, 3, 3)
(15, 15, 15,
12, 11, 4, 2)
(15, 15, 15,
15, 9, 2, 1)
W
(14, 13, 12,
11, 10, 10, 9,
8, 8, 5)
(14, 13, 11, 6,
4, 4, 3, 1, 1, 1)
(13, 11, 8, 6,
4, 3, 3, 3, 1,
1)
(14, 14, 12,
12, 12, 11, 9,
7, 4, 2)
(14, 14, 14,
12, 11, 11, 9,
4, 2, 1)
X
(13, 10, 9, 8,
5, 2, 1)
(16, 13, 13,
13, 13, 6, 1)
(17, 13, 13,
13, 13, 7, 2)
(16, 11, 5, 5,
5, 5, 1)
(17, 12, 5, 5,
5, 5, 2)
Y
(16, 12, 9, 9,
9, 8, 5)
(17, 12, 8, 5,
5, 5, 5)
(16, 11, 8, 6,
6, 6, 3)
(15, 12, 12,
12, 10, 7, 2)
(13, 13, 13,
13, 10, 6, 1)
Z
(13, 13, 13,
13, 13, 10, 7,
4, 1, 1, 1, 1)
(13, 12, 11,
11, 8, 8, 7, 5,
2, 2, 1)
(13, 13, 12,
12, 11, 6, 5, 2,
1, 1)
(13, 13, 12,
10, 7, 7, 7, 7,
7, 4, 2, 1)
(13, 12, 10, 7,
7, 7, 7, 7, 7, 7,
4, 2)
CITY
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Alabaawee, 20212021Basher,
3.6
(3.1) Mahmood , Mahmood, 2019a
(2.1.2)
(3.6.1) 2019aMahmood , Mahmood,
Letter(2)
Letter(1)
Row
(IS)
(2.1.2)IS
,
(3.6.1)
Row
Row
(IS)
Mahmood , Mahmood, 2019b
B
(1-3)B
e
(2-3)B
LSUUL
(3-3)LSUULB
LSULU
(4-3)LSULUB
LSLUL
(5-3)LSLULB
LSLLU
(6-3)LSLLUB
Kirani, 2022b
Kirani, 2022a
:(4.1) ) , 2007Tee(
Bueno, 2013
)(4.2
1
5
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1-4
)3(4.
Kirani
e
Kirani, 2020 b
e
(2.1)(2.1.3)
(3.1.1-3.1.4)
LSLLU
LSLUL
LSULU
LSUUL
(16, 14, 12,
5, 3)
2-4(LSUUL, LSULU, LSLUL , LSLLU )
[5- 2]
LSLLU
LSLUL
LSULU
LSUUL
3-4(LSUUL, LSULU, LSLUL , LSLLU )
(2.3)
LSLLU
LSLUL
LSULU
LSUUL
4-4(LSUUL, LSULU, LSLUL , LSLLU )
Kirani Kirani, 2022b)
e
a) (Kirani, 2022
(Kirani, 2022 b)
Mukai 2019
(1
e
(2.1.1) (2.1.2)(2.1.3)
(2.1.4)
(2.1.5)
(2
e
(2.1.6) (2.1.7)(2.1.8)
(3Satyanarayana, Prasad, 2014
(Rosen, 1999) Hashim, 2022
(4
Mahmood and Mahmood , 2019a Mahmood and Mahmood , 2019b
Alabaawee, 20212021Basher,
KiraniKirani, 2022b
Kirani, 2022a
Ali et al, 2021
Kirani
References:
Alabaawee, A. I. 2021. “New Technologies at Young Tableaux”,
M. Sc. Thesis, Mosul University, Iraq.
Ali , A. M. and Mahmood, A. S. 2020. “The graph of e-abacus
diagram”, WSEAS Trans. on Mathematics, 19(2224-2880), pp.
486-497.
Basher, F. A. 2021. “ New Applications Between Young Diagram
and e-Abacus Diagram”, M. Sc. Thesis, Mosul University, Iraq.
Bondy, J. A. and Murty, U. S. R. 2008. “Graph Theory With
Applications”, American Elsevier, New York.
Bueno , A. C. 2013. “Left circulant matrices with arithmetic
sequence” , South Asian Journal of Mathematics , 3 (5) ,pp. 322 –
325.
Fayers, M. 2007. “ Another runner removal theorem for r-
decomposition numbers of Iwahori-Hecke algebra and q-Schur
algebra”, J. algebra, 310, pp. 396-404.
Hashim, H. R. 2022. “A New Mathematical Representation
Method Using e-Abacus Diagram”, M. Sc. Thesis, University of
Mosul.
James, G. D. 1978. “Some combinatorial results involving Young
diagrams”, Mathematical proceedings of the Cambridge
Philosophical Society, 83, pp..1-10.
Kirani, Y. 2022. “Generation of Plain and Twill Weaves from Left
Circulant Matrices”, International Journal of Research in
Engineering and Science, 10(10), pp. 283-291 .
Kirani, Y. 2022. “Generation of Satin and Sateen Weaves from
Circulant Matrices”, International Journal of Research in
Engineering and Science, 10 (11), pp. 104-110 .
Lovasz , L. , Pelikan , J. and Vesztergombi , K. 2003. “Discrete
Mathematics: Elementary and Beyond, Undergraduate Texts in
Mathematics”, Springer.
Mahmood, A. S. 2011. “On the intersection of Young’s diagrams
core”, Journal of Education and Science, 24, pp. 149-157.
Mahmood, A. S. 2023. “On GCYD-method in e-abacus diagram”,
To appear in Iraqi J. of Science.
Mahmood, A. S. and Al-Hussaini, A. T. 2020. “e-Abacus diagram
rows rearranging technology”, Open Access Library Journal, 7, pp.
1-5.
Mahmood, A. B. and Mahmood , A. S. 2019. “Secret-word by e-
abacus diagram I”, Iraqi J. of Science, 60(3), pp. 638-646.
Mahmood , A. B. and Mahmood, A. S. 2019. “Secret-text by e-
abacus diagram II”, Iraqi J. of Science, 60(4), pp. 840- 846.
Mahmood , A. S. and Mohammed , H. S. 2011. “Radical Young's
Diagrams Core” , Journal of Education and Science 24(1), pp. 72-
92 .
Majeed, I. , Ayyed, E. and Mahdi, N. 2022. “New Measurement
Technique for Complex Permittivity in Millimeter-Wave Band
Using Simple Rectangular Waveguide Adapters”, J. Electromagn.
Eng. Sci., 22(6), pp.616-621.
Mathas, A. 1999 . “Iwahori-Hecke Algebras and Schur Algebras
of the Symmetric Group” (Vol. 15) . University Lecture Series.
Mukai, Y. 2019. “Dielectric Properties of Cotton Fabrics and Their
Applications”, Ph. D. Dissertation, Raleigh, North Carolina, USA.
Rosen, K. H. 1999. “Handbook of Discrete and Combinatorial
Mathematics”, CRC Press.
Satyanarayana B. and Prasad, K. S. 2014. “Discrete Mathematics
and Graph Theory”, PHI Learning Private limited, 2end edition,
Delhi.
Tee , G. J. 2007. “Eigenvectors of Block Circulant and
Alternating Circulant Matrices”, New Zealand Journal of Research
in Engineering and Science, 36, pp. 195-211.
Zhang , J. , Pan , R. , Wang, J. , Gao, W. and Han, Y. 2017. “An
efficient method for density measurement for high-tightness woven
fabrics” , Textile Research Journal , 87(3), pp. 1-11.
Abstract
This thesis has three objectives. The first is to complete what
Fayres, Mahmood, and Mohammed each independently did in adding a
column and then columns to the e-abacus diagram, so that we could add a
row and then rows on the same diagram this time and know the
requirements for it. The second objective is to locate a new movement on
the diagram that has never been used before, to characterize it, and to
determine what future possibilities it presents.
The ultimate and most significant goal, which was to find an industrial
application that could profit from them, was served by both of the
aforementioned objectives. We achieved this through the work that
Kirani presented in his research on a textile application in 2022, which
was based on a model submitted for a doctoral dissertation in the United
States of America by Mukai in 2019.
University of Mosul
College of Education
For Pure Science
Some Application of Specific Movements on
e- Abacus Diagram
Jwan Khairi Khaleel Ismaeel
M.Sc. Thesis
Mathematics
Supervised by
Prof.
Dr. Ammar Seddiq Mahmood
A.D 2023 A.H 1444
Some Application of Specific Movements on
e- Abacus Diagram
A Thesis Submitted
By
Jwan Khairi Khaleel Ismaeel
To
The Council of College of Education for Pure Science University of
Mosul In Partial Fulfillment of Requirements for
the Degree of M.Sc.
In
Mathematics
Supervised by
Prof.
Dr. Ammar Seddiq Mahmood
A.D 2023 A.H 1444
