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## Abstract

We be dealt the letters of Syriac language as it is natural numbers, to enter the diagram of James ( A) to the theory of partition, this process will have uses in our daily lives and in confidential correspondence.
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Syriac Letters and James Diagram (A)
Hadil H. Sami1, Prof. Dr. Ammar S. Mahmood2
1Department of Mathematics, College of Education, University of Al-Hamdaniya, Mosul, Iraq.
2 Department of Mathematics, College of Education for Pure Science, University of Mosul, Mosul, Iraq.
ABSTRACT
Will be dealt with the letters of Syriac language as it is natural numbers, to enter the diagram of James )A( to
the theory of partition, this process will have uses in our daily lives and in confidential correspondence.
Keywords: Partition theory, Beta numbers, Syriac Letters.
1. INTRODUCTION
The aim of the study is how to use the Syriac language as a secret message between two people or more.Syriac language
is a Semitic language derived from the Aramaic language which appeared in the first millennium BC, and in the sixth
century BC Syriac language has become the only language of communication in the (fertile crescent) region, till after the
birth of Christ this language gained its new name (Syriac) in the fourth century [5,7].
This language like other Semitic languages has multiple letters which is 22 letters, three of this letters are vowels, but
the rest of the letters are silent, this letters are as follows:
.
The letters do not appear but replace it with meaningless numbers if this message read by a stranger person, from here
the idea started where we saw that James' diagram (A) could help us. First of all, we will explain what James’s diagram
is and then begin the process of linking with Syriac characters. Let be a non-negative integer, a composition μ of r is
a sequence μ=1 ,2, nof non-negative integers suchthat =j
n
j=1 = r, . For example, if = 4, the
following sequences are compositions:
4,3,1,2,2,1,3,2,1,1,1,2,1,1,1,2,1,1,1,1.
The composition μ is said to be a partition of r if j  j+1 , j 1. By using the previous example in the case of
r = 4, the following sequences satisfy the condition of partition:
4,3,1,2,2,2,1,1,1,1,1,1.
Let be a number of redundant part of the partition of r, then we have =1,2,,n= 1
1,2
2,,f
fsuch
that: =j
n
j=1 = l
lf
l=1 , .
β - numbers was defined by; see James in : "Fix μ is a partition of r, choose an integer b greater than or equal to
the number of parts of and definei=i+ b i, 1ib. The set 1,2,,bis said to be the set of β
- numbers for µ. For example if we have the partition μ= (6,5,2,2,1) and b = 5 b=5 then β - numbers for partition μ
will be:
* ، ، ، ، ،* ، ، ، ،* ، ـ، ـ ، ـ ، ــ ،
، ـ ، ـ ، ، ، ، ،
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Where every β numbers will be represented by a bead (●) which takes its location in diagram (A) and in case of
nonexistence of β - numbers, then the value in diagram (A) will be represented by a blank )-(. Returning to the previous
example in the case of =6,5,2,2,1and b = 5, then the set of β numbers are 10,8,4,3,1 and diagram )A) where
e = 2 will be:
and if e = 3
It is possible from diagram (A) we can know the partition that belong to it , by numbering the blanks which precedes
the beads In ascending order from left to right, where the number of blanks preceding any bead is represented by one of
the elements μ, for example, the number of blanks preceding the first bead will represent the value of n, and the
number of blanks preceding the second bead represents n1, thus, until the last bead in diagram (A), all the blanks in
the diagram preceding this bead will be represented by 1. For example, we have the following diagram (A) we will
find its own partition as shown below:
μ=12,8,7,5, 42, 1. Many papers that talk about specific types of movements, see [3,6].
2. THE RELATION BETWEEN SYRIAC WORDS AND JAMES DIAGRAM (A)
In this part we will try to find a suitable way to write each letter of the Syriac language according to diagram (A). The
focus was on choosing a fixed (e) and an equal number of rows for each letter, after the study it was found that e = 7 and
7 of the rows is the best choice as follows:
1
0
3
2
5
4
7
6
9
8
11
10
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2
1
0
5
4
3
8
7
6
11
10
9
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2
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1
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4
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-7
-6
-9
-8
-12
-11
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The following diagrams are for the letters that come at the end of the word, as well as we have made clips for the letters
() and () with the rest of the letters for easy connectivity when writing the word.
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International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
Page | 58
International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
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Here we will have the following question: If we want to write a word, it is likely to consist of a number of letters, thus
what is the partition that denotes that word?
For example, we have the words () and (), the partition and James diagram are as follows:

= (995,98,928,872,803,77,724,66,62,572,56,45,404,285,6)
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Through what has been explained, the process of writing a partition by the numbering of the blank in each row of the
word from left to right will be arranged in ascending order, thus the first row of the first letter from the left it will be
according to the known rule for finding a partition. As for the first row of the second letter, the value (e) will have a
large role and then the number of beads located in the first row of the first letter to the left, if we move to the third letter
in the first row, the value of (2e) will have the largest role deleted from it number of beads located in the first row of the
first and second letters to the left. Thus, we get to the first row of the last letter it will be as much as (e (the number of
letters - 1)) subtracted from it the number of beads in the first row of letters which preceded the last letter. Now, if we
move to the second row of the first letter to the left, it will be (e (number of letters - 1)) subtracted from it the number of
the beads that preceded it in the first row of all letters except the same letter considering that the partition was basically
calculated previously. This process will be repeated with the rest of the rows and cases, where we will always subtract
the number of beads located before the same site except for the same letter, so through the above, the rule of this will be:
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Here, must be attention before everything on the form of the letters such as ، ، ... when used it with the rest of the
letters for the purpose of forming the word here we must shift the letters to the top and in this case we will delete (14)
blanks of each 1 ,,2, , n of each letter. For example, when connecting the two letters and to form the section
 ,here we need to make the letterin parallel with the letter , in this case we will re-write the partition of the
letter which is (308,244) so that after deleting (14) blanks of each μ are (168,104) and thus this will be the new
partition of the letter, and in the same way with the rest of the letters. In the same way we will try to find the general
rule to write a sentence, and for that the rule is:
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REFERENCES
. G. James. (1978); “Some combinatorial results involving Young diagrams” , Math. Proc. Cambridge Phil. Soc., Vol. 83, 1-
10.
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no.3, 143 -159.
. A. S. Mahmood and S. S. Ali, (2014);” (Upside-down o direct rotation)β - numbers , American J. of Math. and Stat. Vol. (4),
no.2, 58-64.
. A. Mathas. (1999); “Iwahori - Hecke Algebras and Schur Algebras of the Symmetric Groups ", Amer. Math. Soc., University
Lecture Series, Vol. 15.
. J.Messo. (2005); “Syriac / Aramaic Language and Culture” , www.midyatcity.com.
. E. F. Mohommed, H. Ibahim, N. Ahmad and A. S. Mahmood. (2016);” Nested chain movement of length 1 of beta-number, in
James abacus diagram” Indoe Global J. of Pure and Applied Mathematics, Vol. 12,no. 4, 2953-2969
. R.Rollinger. (2006); “The Terms Assyria and Syria Again ”, JNES Vol. 65, no. 4.
.