Symmetric generating functions and permanents of totally nonnegative matrices

Algebra Seminar
Thursday, March 17, 2022 - 12:00pm for 1 hour (actually 50 minutes)
Skiles 006
Mark Skandera – Lehigh University –
Ashley K. Wheeler

For each element $z$ of the symmetric group algebra we define a symmetric generating function

$Y(z) = \sum_\lambda \epsilon^\lambda(z) m_\lambda$, where $\epsilon^\lambda$ is the induced sign

character indexed by $\lambda$. Expanding $Y(z)$ in other symmetric function bases, we obtain

other trace evaluations as coefficients. We show that we show that all symmetric functions in

$\span_Z \{m_\lambda \}$ are $Y(z)$ for some $z$ in $Q[S_n]$. Using this fact and chromatic symmetric functions, we give new interpretations of permanents of totally nonnegative matrices.

For the full paper, see