切换群、homomesy和Razumov-Stroganov对应
The toggle group, homomesy, and the Razumov-Stroganov correspondence
摘要：
Razumov-Stroganov对应是统计物理学和组合数学之间的一个重要联系，由L。Cantini和A. Sportiello将半无限圆柱上O（1）稠密环模型的基态本征向量与完全填充环的精细枚举联系起来，这些环是具有交替符号矩阵的双射。本文用偏序集、肘节群和同态来重新表述这个证明的一个关键组成部分，并证明了两个关于一般偏序集的新的同态结果，我们希望这些结果具有更广泛的意义。
英文摘要：
The Razumov-Stroganov correspondence, an important link between statistical physics and combinatorics proved in 2011 by L. Cantini and A. Sportiello, relates the ground state eigenvector of the O(1) dense loop model on a semi-infinite cylinder to a refined enumeration of fully-packed loops, which are in bijection with alternating sign matrices. This paper reformulates a key component of this proof in terms of posets, the toggle group, and homomesy, and proves two new homomesy results on general posets which we hope will have broader implications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
