In this paper, we present a new identity for derangements, and as a corollary, we have a combinatorial proof of the irreducibility of the standard representation of symmetric groups

Author Bio

I am an honour student at University of New SouthWales, Australia. This paper was written while I was taking a course in grouprepresentaion. While I was proving the irreducibility of thestandard representation of the symmetric groups, I discoverd a new and interesting identity for derangements and Bellnumbers. After graduation thisyear, I plan to pursue a PhD in Pure Mathematics.