发表机构
The Open University（开放大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过结合多米诺方法与Bóna的装饰词对思想，并引入shuffle自动机处理交错，将1324-回避排列的增长常数上界改进至13.167248。
AI 中文摘要
我们证明$\text{gr}(\text{Av}(1324))\leq 13.167248$。这是通过将Bevan、Brignall、Elvey Price和Pantone使用“多米诺”的方法与Bóna早期上界中利用带有额外限制的装饰词对的思想相结合而实现的。更具体地说，我们将Bevan等人的任意交错替换为更类似于Bóna的交错。我们的方法使用shuffle自动机来处理交错，并且该方法有潜力提供比本文所建立的更好的上界。为了估计可能的shuffle数量，我们使用多米诺上的两个关键统计量：内部点的数量（即既不是从左到右的最小值也不是从右到左的最大值的点），以及内部点的游程数量。
英文摘要
We show that $\text{gr}(\text{Av}(1324))\leq 13.167248$. This is achieved by combining the approach of Bevan, Brignall, Elvey Price and Pantone using the `domino', with ideas from earlier upper bounds by Bóna using pairs of decorated words with additional restrictions. More specifically, we replace the arbitrary interleavings of Bevan et. al. with interleavings more like those of Bóna. Our method uses shuffle automata to handle the interleavings, and this method has the potential to provide better upper bounds than the one established here. To estimate how many shuffles are possible, we use two key statistics on dominoes: the number of internal points (that is, points that are neither left-to-right minima not right-to-left maxima), and the number of runs of internal points.
Comments32 pages
