In the context of the shuffle theorem, many classical integer sequences appear with a natural refinement by two statistics q and t, like the Catalan and Schröder numbers. In particular, the bigraded Hilbert series of diagonal harmonics is a q, t-analog of (n + 1)^(n−1) (and can be written in terms of symmetric functions via the nabla operator). The motivation for this talk is the observation that at q = −1, this q, t-analog becomes a t-analog of Euler numbers, a famous integer sequence that counts alternating permutations. We prove this observation via a more general statement, that involves the Delta operator on symmetric functions (on one side), and new combinatorial statistics on permutations involving peaks and valleys (on the other side).
