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A proof of the $4$-variable Catalan polynomial of the Delta conjecture. (arXiv:1609.03497v2 [math.CO] UPDATED)
来源于:arXiv
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 implies the non-compositional
version) that states that the coefficient of $s_{r,1^{n-r}}$ in the expression
$\Delta_{h_\ell} \nabla C_\alpha$ is equal to a weighted sum over decorated
Dyck paths. 查看全文>>