## The Delta Conjecture at $q = 1$

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**369**(2017), 7509-7530 Request permission

## 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 of Haglund, Remmel, and Wilson 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.## References

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## Additional Information

**Marino Romero**- Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093
- Email: mar007@ucsd.edu
- Received by editor(s): September 14, 2016
- Received by editor(s) in revised form: November 23, 2016
- Published electronically: June 27, 2017
- Additional Notes: This research was supported by NSF grant 1362160
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**369**(2017), 7509-7530 - MSC (2010): Primary 05E05, 05E10, 05Exx
- DOI: https://doi.org/10.1090/tran/7140
- MathSciNet review: 3683116