The Relation Between the Alternating Group and Standard Row Young’s Diagrams

This study tackles the relationship between the alternating group 14An"> and young’sdiagrams concerning standard rows. The study has been divided into two stages… <strong>First</strong>, even permutations have been found depending on the conception of partition 14خ¼"> through formulating an algorithm for this purpose. <strong>Secondly</strong>, the relationship between the cycle length and partition 14خ¼"> has been found.<br /> 14د¨ .1"> <strong> </strong><strong>Introduction:</strong><br /> 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:<br /> 144, 3,1, 2,2, 1,3,2,1,1,1,2,1,1,1,2,1,1,1,1"> .