Jesse Campion Loth

How many ways are there to write a given permutation as a product of m transpositions (i_1, j_1) (i_2, j_2) \dots (i_m, j_m)? For example, there are three ways to write (1,2,3) as a product of two transpositions: (1,2)(1,3), (1,3)(2,3) and (2,3)(1,2)...

Products of permutations are used to model problems in fields ranging from representation theory and algebraic geometry to topological graph theory. I will show how probability can be used to study such problems, with a focus on how graphs may be...