« search calendars« Graduate Combinatorics Seminar
« How Many Ways Can a Permutation in S_n be Written as a Product of k Transpositions?
How Many Ways Can a Permutation in S_n be Written as a Product of k Transpositions?
February 26, 2020, 12:15 PM - 1:15 PM
Location:
Mathematics Graduate Student Lounge -- 7th Floor
Rutgers University
Hill Center
Mathematics Department
110 Frelinghuysen Road
Piscataway, NJ 08854
Nathan Mehlhop, Rutgers University
To answer the question in the title, we will develop a systematic method for calculating these numbers using the adjacency matrices of certain directed graphs whose vertices are the conjugacy classes of S_n. I will mumble without proof some connections to the representation theory of S_n and to symmetric functions, and then prove a few identities using facts about Ferrers diagrams.