Permutations (Pt. VI Alternate Definitions of the Sign of a Permutation cont.)
Point of post: This is a literal continuation of this post. I just hate when that dark grey to light grey thing happens. Just pretend that there was no lapse in the posts
And so we continue…
Permutations (Pt. VI Alternate Definitions of the Sign of a Permutation)
Point of post: In this post we point out two different, but commonly used, definitions for the sign of a permutation and show that they’re equivalent to the one given here. Namely, the definitions given by the polynomial commonly denoted 
Motivation
Often in abstract and linear algebra books the definition of the sign of a permutation is not the same as the one given by me in the last post. This can be patently disturbing, since one will undoubtedly wonder “Are these the same definition, just said different?” and maybe more to the point “Why did they use this definition? Is it ‘better’, and if so, in what way?” I hope to answer these questions (to within the limitations of my time and the size of these posts) for two of the most commonly found definitions of the sign of a permutation.
About me
My name is Alex Youcis. I am currently a senior at the University of Maryland, College park getting my bachelor’s in mathematics. Before I came to UMD I was a math major at Drexel University in Philadelphia, Pennsylvania. I was born and raised in Lititz, Pennsylvania, a small town near Lancaster.
As is probably clear, I really enjoy doing math. It’s a passion for me, and I don’t means this in the weekend-hobby sense, I can’t imagine doing anything else other than mathematics. That said, I’m not one of those space cadets one often sees wandering around math departments, trying to solve others problems, or perpetrating some other equally creepy shenanigans. No, while math is a gargantuan aspect of my life, there are many, many other things that interest me. Perhaps the most consuming of these is my love of music. I find it difficult to go even one day without my iPhone, or grooveshark.com If you want to say something to me in the car, you have about eight seconds before my iPhone is plugged in and we’ve set sail on a musical adventure. I have hundreds, upon hundreds of bands that I intensely love, but at the time of writing I can emphatically say that Regina Spektor is my favorite artist–the woman is a musical Gauss. I also love dogs, friends, conversations about things, craft beer and the occasional online comic.
If you’d like to know anything about this blog see the pertinent page in all its splendorous glory.
If you have any questions regarding myself, math, music, or anything else feel free to e-mail me at alex.youcis@gmail.com
Current Course List:
Advanced Microeconomics
Numerical Analysis–uses Suli and Meyers
Riemann Surfaces–Uses Varolin. This is available, in near entirety, for free here.
Algebraic Number Theory–Using various course notes, including those of Milne. The course website is here.
Representation Theory of 
