I am an honour student at University of New South Wales, Australia. This paper was written while I was taking a course in group representaion. While I was proving the irreducibility of the standard representation of the symmetric groups, I discoverd a new and interesting identity for derangements and Bell numbers. After graduation this year, I plan to pursue a PhD in Pure Mathematics.
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Faculty Sponsor: Catherine Greenhill, School of Mathematics, University of New South Wales, Sydney, Australia