A proof of the $4$-variable Catalan polynomial of the Delta conjecture

arXiv: Combinatorics, 2016.

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Abstract:

In The Delta Conjecture (arxiv:1509.07058), Haglund, Remmel and Wilson introduced a four variable $q,t,z,w$ Catalan polynomial, so named because the specialization of this polynomial at the values $(q,t,z,w) = (1,1,0,0)$ is equal to the Catalan number $frac{1}{n+1}binom{2n}{n}$. We prove the compositional version of this conjecture (which...More

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