论文标题
彩色顶点型号和$ k $ - 阿兹台克钻石的使用
Colored vertex models and $k$-tilings of the Aztec diamond
论文作者
论文摘要
我们研究阿兹台克钻石的$ k $ litings（$ k $ tillings of Domino Tilings of Domino Tilings）的等级$ M $。我们为每种$ k $ friping分配一个重量，具体取决于某些类型的多米诺蛋白的数量以及瓷砖之间的“互动”数量。采用早期工作中引入的有色顶点模型来研究超对称LLT多项式，我们计算了$ k $ - 使用的生成多项式。然后，我们证明了一些大约$ k $的组合结果，包括没有互动的$ k $使用和$ 1 $的使用，我们计算了$ t = 0 $和$ t \ rightarrow \ rightarrow \ rightarrow \ infty $的北极曲线。我们还提出了一些六角形的lozenge $ k $，并以$ t = 0 $计算砖的北极曲线。
We study $k$-tilings ($k$-tuples of domino tilings) of the Aztec diamond of rank $m$. We assign a weight to each $k$-tiling, depending on the number of dominos of certain types and the number of "interactions" between the tilings. Employing the colored vertex models introduced in earlier work to study supersymmetric LLT polynomials, we compute the generating polynomials of the $k$-tilings. We then prove some combinatorial results about $k$-tilings, including a bijection between $k$-tilings with no interactions and $1$-tilings, and we compute the arctic curves of the tilings for $t=0$ and $t\rightarrow\infty$. We also present some lozenge $k$-tilings of the hexagon and compute the arctic curves of the tilings for $t=0$.
