The Delta Conjecture at $q=1$

Abstract

We use a weight-preserving, sign-reversing involution to find a combinatorial expansion of $\Delta_{e_k} e_n$ at $q=1$ in terms of the elementary symmetric function basis. We then use a weight-preserving bijection to prove the Delta Conjecture at $q=1$. The method of proof provides a variety of structures which can compute the inner product of $\Delta_{e_k} e_n|_{q=1}$ with any symmetric function.