Pinnacle sets of permutations

Given a permutation $w$, we can graph $w$ by plotting points $(i,w(i))$ for $i=1,\dots, n$ and connecting $(i,w(i))$ to $(i+1,w(i+1))$ by straight line segments. From this perspective, peaks of $w$ record the indices of local maxima and pinnacles record the values of local maxima. Peaks are a well-studied statistic of permutations, and, in recent years, pinnacles and admissible pinnacle sets for the type A symmetric group have been widely studied. In this talk, we will define pinnacle sets of signed permutations and the analogous concept for Stirling permutations. We will answer several enumerative questions about admissible pinnacle sets in both settings. Then we will conclude with some open questions about the values of local maxima for these families of permutations.

Bio
 https://sites.google.com/view/girkirby/