A refined Razumov–Stroganov conjecture
A refined Razumov–Stroganov conjecture
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改进的拉祖莫夫-斯特罗加诺夫猜想
DOI：
10.1088/1742-5468/2004/08/p08009
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
P. Francesco
中科院分区：
文献类型：
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作者：
P. Francesco
通过将O（1）模型的monodromy矩阵的基态与所谓的精化交替符号矩阵（即第一行具有规定的配置）以及与正方形网格上的精化全填充环配置相关联，我们扩展了将O（1）自旋链的基态与交替符号矩阵相关联的Razumov-Stroganov猜想，跟踪环路连通性和它们的顶行的配置。我们还猜想这基态和完善的完全对称的自互补平面分区之间的直接关系，即，在他们的制定为一套不相交的晶格路径，与规定的最后步骤的所有路径。
We extend the Razumov–Stroganov conjecture relating the groundstate of the O(1) spin chain to alternating sign matrices by relating the groundstate of the monodromy matrix of the O(1) model to the so-called refined alternating sign matrices, i.e. with prescribed configuration of their first row, as well as to refined fully-packed loop configurations on a square grid, keeping track both of the loop connectivity and of the configuration of their top row. We also conjecture a direct relation between this groundstate and refined totally symmetric self-complementary plane partitions, namely, in their formulation as sets of non-intersecting lattice paths, with the prescribed last steps of all paths.