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arxiv: 1609.04865 · v1 · pith:IP6JZZU6new · submitted 2016-09-15 · 🧮 math.CO

The Delta Conjecture at q=1

classification 🧮 math.CO
keywords deltaconjecturefunctionsymmetricweight-preservingbasisbijectioncombinatorial
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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.

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