The Delta Conjecture at 𝑞=1

Romero, Marino

doi:10.1090/tran/7140

The Delta Conjecture at

Author: Marino Romero
Journal: Trans. Amer. Math. Soc. 369 (2017), 7509-7530
MSC (2010): Primary 05E05, 05E10, 05Exx
DOI: https://doi.org/10.1090/tran/7140
Published electronically: June 27, 2017
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Abstract:

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

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