Recursions for rational q,t-Catalan numbers
Recursions for rational q,t-Catalan numbers
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有理 q,t-Catalan 数的递归
DOI：
10.1016/j.jcta.2020.105237
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Vazirani, Monica
中科院分区：
文献类型：
--
作者：
Gorsky, Eugene;Mazin, Mikhail;Vazirani, Monica
本文给出了一个简单的二元序列递归算法，它可以计算相对素和非相对素的有理q，t-Catalan幂级数。它受B的启发，但与递归不完全相同。Elias，M. Hogancamp和A. Mellit，在他们的研究中获得的链接同源性。我们还比较了我们的递归与Hogancamp-Mellit的递归，并验证了N，M-环面环的Khovanov-Rozansky同调与一般正N，M的有理q，t-Catalan幂级数之间的联系。
We give a simple recursion labeled by binary sequences which computes rational q, t-Catalan power series, both in relatively prime and non relatively prime cases. It is inspired by, but not identical to recursions due to B. Elias, M. Hogancamp, and A. Mellit, obtained in their study of link homology. We also compare our recursion with the Hogancamp-Mellit's recursion and verify a connection between the Khovanov-Rozansky homology of N, M-torus links and the rational q, t-Catalan power series for general positive N, M.