论文标题
二维的加权单词，我：Bressoud的算法作为能量转移
Weighted words at degree two, I: Bressoud's algorithm as an energy transfer
论文作者
论文摘要
在最近的一篇论文中，我们概括了Siladić在他对$ a_2^{（2）} $类型标准模块的研究中所说的分区身份。证明使用的加权单词具有任意数量的原色数量和从这些原色获得的所有次要颜色，以及Bressoud的Bookeding for Schur的分区身份的全新变体。在本文中，我们在统计力学框架中分析了布雷索德算法的这种变体，在该框架中，根据某些州之间的某些属性，整数分区被视为共有的能量量。这种观点使我们能够通过考虑更一般的差异条件的更普遍的家族来概括先前的结果。例如，我们将Siladić身份推广到过度分区。在第二篇论文中，我们将此结果连接到Glaisher定理，并提供一些应用以升级一个完美的晶体。
In a recent paper, we generalized a partition identity stated by Siladić in his study of the level one standard module of type $A_2^{(2)}$. The proof used weighted words with an arbitrary number of primary colors and all the secondary colors obtained from these primary colors, and a brand new variant of the bijection of Bressoud for Schur's partition identity. In this paper, the first of two, we analyze this variant of Bressoud's algorithm in the framework of statistical mechanics, where an integer partition is viewed as an amount of energy shared, according to certain properties, between several states. This viewpoint allows us to generalize the previous result by considering a more general family of minimal difference conditions. For example, we generalize the Siladić identity to overpartitions. In the second paper, we connect this result to the Glaisher theorem and give some applications to level one perfect crystals.
