A q-Analog of the Hook Walk Algorithm for Random Young Tableaux
A q-Analog of the Hook Walk Algorithm for Random Young Tableaux
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随机年轻 Tableaux 的 Hook Walk 算法的 q 模拟
DOI：
10.1023/a:1022423901412
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发表时间：
1993
影响因子：
0.8
通讯作者：
S. Kerov
中科院分区：
文献类型：
--
作者：
S. Kerov
定义了一种称为q-hook遍历的概率算法。对于给定的Young图，它通过添加一个具有概率的随机框来产生一个新的图，依赖于一个正参数q。无限Young表空间中相应的马尔可夫链与Jones的结不变量密切相关，通过Hecke代数的迹来构造。对于q = 1，该算法本质上是Greene， Nijenhuis和Wilf的hook walk。同时考虑了杨格图的q-钩公式和q-变形。
A probabilistic algorithm, called the q-hook walk, is defined. For a given Young diagram, it produces a new one by adding a random box with probabilities, depending on a positive parameter q. The corresponding Markov chain in the space of infinite Young tableaux is closely related to the knot invariant of Jones, constructed via traces of Hecke algebras. For q = 1, the algorithm is essentially the hook walk of Greene, Nijenhuis, and Wilf. The q-hook formula and a q-deformation of Young graph are also considered.