This study tackles the relationship between the alternating group 14An"> and young’sdiagrams concerning standard rows. The study has been divided into two stages… First, even permutations have been found depending on the conception of partition 14خ¼"> through formulating an algorithm for this purpose. Secondly, the relationship between the cycle length and partition 14خ¼"> has been found.
14د¨ .1"> Introduction:
Let 14n"> be a non-negative integer, a composition 14 خ¼"> of 14n"> is a sequence 14 خ¼=خ¼1 ,خ¼2, ⋯خ¼r "> of non-negative integers such that 14 خ¼=j=1rخ¼j =n"> , [5]. For example, if 14n=4"> , the following sequences are compositions:
144, 3,1, 2,2, 1,3,2,1,1,1,2,1,1,1,2,1,1,1,1"> . |
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I.N. Herstein “ Topics in Algebra” edition university of Chicago 1975.
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[1]
|
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T. W. Judson & Stephen F. “ Abstract algebra theory and applications” Austin state university, 2010
|
[2]
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R. Keown “ An introduction to Group Representation Theory “ Academic . press, New York, 1975
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[3]
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M.W. Kirson “Introductory Algebra for Physicists” ch. Irreducible representations , 2013.
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[4]
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A. Mathas “ Iwahori – Hecke Algebras and Schur Algebras of the Symmetric Groups”, Amer.Math. Soc., University Lecture Series, Vol.15, 1999
|
[5]
|
|
W. R. Scott “ Group theory” Dover publications, 1987
|
[6]
|
|
Y. Zhao “Young Tableaux and the Representations of the Symmetric Group”Harvard College Mathematics Review 2(2), 33-45, 2008.
|
[7]
|
|
I.N. Herstein “ Topics in Algebra” edition university of Chicago 1975.
|
[1]
|
|
T. W. Judson & Stephen F. “ Abstract algebra theory and applications” Austin state university, 2010
|
[2]
|
|
R. Keown “ An introduction to Group Representation Theory “ Academic . press, New York, 1975
|
[3]
|
|
M.W. Kirson “Introductory Algebra for Physicists” ch. Irreducible representations , 2013.
|
[4]
|
|
A. Mathas “ Iwahori – Hecke Algebras and Schur Algebras of the Symmetric Groups”, Amer.Math. Soc., University Lecture Series, Vol.15, 1999
|
[5]
|
|
W. R. Scott “ Group theory” Dover publications, 1987
|
[6]
|
|
Y. Zhao “Young Tableaux and the Representations of the Symmetric Group”Harvard College Mathematics Review 2(2), 33-45, 2008.
|
[7]
|
|
.N. Herstein “ Topics in Algebra” edition university of Chicago 1975.
|
[1]
|
|
T. W. Judson & Stephen F. “ Abstract algebra theory and applications” Austin state university, 2010
|
[2]
|
|
R. Keown “ An introduction to Group Representation Theory “ Academic . press, New York, 1975
|
[3]
|
|
M.W. Kirson “Introductory Algebra for Physicists” ch. Irreducible representations , 2013.
|
[4]
|
|
A. Mathas “ Iwahori – Hecke Algebras and Schur Algebras of the Symmetric Groups”, Amer.Math. Soc., University Lecture Series, Vol.15, 1999
|
[5]
|
|
W. R. Scott “ Group theory” Dover publications, 1987
|
[6]
|
|
Y. Zhao “Young Tableaux and the Representations of the Symmetric Group”Harvard College Mathematics Review 2(2), 33-45, 2008.
|
[7]
|
|
I.N. Herstein “ Topics in Algebra” edition university of Chicago 1975.
|
[1]
|
|
T. W. Judson & Stephen F. “ Abstract algebra theory and applications” Austin state university, 2010
|
[2]
|
|
R. Keown “ An introduction to Group Representation Theory “ Academic . press, New York, 1975
|
[3]
|
|
M.W. Kirson “Introductory Algebra for Physicists” ch. Irreducible representations , 2013.
|
[4]
|
|
A. Mathas “ Iwahori – Hecke Algebras and Schur Algebras of the Symmetric Groups”, Amer.Math. Soc., University Lecture Series, Vol.15, 1999
|
[5]
|
|
W. R. Scott “ Group theory” Dover publications, 1987
|
[6]
|
|
Y. Zhao “Young Tableaux and the Representations of the Symmetric Group”Harvard College Mathematics Review 2(2), 33-45, 2008.
|
[7]
|
|
I.N. Herstein “ Topics in Algebra” edition university of Chicago 1975.
|
[1]
|
|
T. W. Judson & Stephen F. “ Abstract algebra theory and applications” Austin state university, 2010
|
[2]
|
|
R. Keown “ An introduction to Group Representation Theory “ Academic . press, New York, 1975
|
[3]
|
|
M.W. Kirson “Introductory Algebra for Physicists” ch. Irreducible representations , 2013.
|
[4]
|
|
A. Mathas “ Iwahori – Hecke Algebras and Schur Algebras of the Symmetric Groups”, Amer.Math. Soc., University Lecture Series, Vol.15, 1999
|
[5]
|
|
W. R. Scott “ Group theory” Dover publications, 1987
|
[6]
|
|
Y. Zhao “Young Tableaux and the Representations of the Symmetric Group”Harvard College Mathematics Review 2(2), 33-45, 2008.
|
[7]
|
|
I.N. Herstein “ Topics in Algebra” edition university of Chicago 1975.
|
[1]
|
|
T. W. Judson & Stephen F. “ Abstract algebra theory and applications” Austin state university, 2010
|
[2]
|
|
R. Keown “ An introduction to Group Representation Theory “ Academic . press, New York, 1975
|
[3]
|
|
M.W. Kirson “Introductory Algebra for Physicists” ch. Irreducible representations , 2013.
|
[4]
|
|
A. Mathas “ Iwahori – Hecke Algebras and Schur Algebras of the Symmetric Groups”, Amer.Math. Soc., University Lecture Series, Vol.15, 1999
|
[5]
|
|
W. R. Scott “ Group theory” Dover publications, 1987
|
[6]
|
|
Y. Zhao “Young Tableaux and the Representations of the Symmetric Group”Harvard College Mathematics Review 2(2), 33-45, 2008.
|
[7]
|
|
I.N. Herstein “ Topics in Algebra” edition university of Chicago 1975.
|
[1]
|
|
T. W. Judson & Stephen F. “ Abstract algebra theory and applications” Austin state university, 2010
|
[2]
|
|
R. Keown “ An introduction to Group Representation Theory “ Academic . press, New York, 1975
|
[3]
|
|
M.W. Kirson “Introductory Algebra for Physicists” ch. Irreducible representations , 2013.
|
[4]
|
|
A. Mathas “ Iwahori – Hecke Algebras and Schur Algebras of the Symmetric Groups”, Amer.Math. Soc., University Lecture Series, Vol.15, 1999
|
[5]
|
|
W. R. Scott “ Group theory” Dover publications, 1987
|
[6]
|
|
Y. Zhao “Young Tableaux and the Representations of the Symmetric Group”Harvard College Mathematics Review 2(2), 33-45, 2008.
|
[7]
|
|
