London Algebra Colloquium abstract

New formulae for structure constants in the symmetric group

Dr Amarpreet Rattan (Birkbeck), 7th February 2013


In 1980 Boccara showed that the number of times an odd permutation in Sn can be written as a product of an n-cycle and an (n−1)-cycle is independent of the permutation chosen. We give a generalization of this result using two different methods: the character theory of Sn, and a combinatorial inductive argument. Our methods lead to other enumerative formulae and applications. In particular, if time permits, we give an application to the recent notion of separable permutations by Bernardi, Du, Morales and Stanley.