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The Delta Conjecture at $ q = 1$


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 $ 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\vert _{q=1}$ with any symmetric function.


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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

DOI: https://doi.org/10.1090/tran/7140
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
Article copyright: © Copyright 2017 American Mathematical Society

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