** Speaker:** Eric Egge, Carleton College

** Title:** Snow Leopard Permutations, Even Knots, Odd Knots, Janus Knots, and Restricted Catalan Paths

** Abstract: **
Snow leopard permutations are the permutations the (complete) Baxter permutations induce on their odd
entries, when their even entries form a doubly alternating permutation. Thanks to some work four of my
students did last year, we know (among other things) that there are C_n snow leopard permutations of length
2n+1, we have a simple bijection between these permutations and the Catalan paths of length 2n, and we know
that the snow leopard permutations preserve parity. In this talk I will fill in some the details I've left
out above, and I'll describe some connections between certain classes of restricted Catalan paths and the
permutations snow leopard permutations induce on their even and odd entries. This is joint work with Ben
Caffrey, Greg Michel, Kailee Rubin, Jon Ver Steegh.