Directed Animals and Gas Models Revisited
Directed Animals and Gas Models Revisited
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重新审视定向动物和气体模型
DOI：
10.37236/989
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
J. Marckert
中科院分区：
文献类型：
--
作者：
Y. L. Borgne;J. Marckert
在本文中，我们重新使用气体模型的有向动物的枚举。我们表明，存在一个自然的建设随机定向动物在任何有向图与粒子系统-气体模型与最近的排斥-这解释combinatorialy的正式联系已知的气体模型的密度和生成函数的定向动物计数根据面积。这为计算按面积计数的有向动物的生成函数提供了新的方法，并在正方形格的特殊情况下引出了新的组合结果和问题。还展示了与有向动物相关的气体模型，该模型根据任何有向图上的面积和周长进行计数。
In this paper, we revisit the enumeration of directed animals using gas models. We show that there exists a natural construction of random directed animals on any directed graph together with a particles system – a gas model with nearest exclusion – that explains combinatorialy the formal link known between the density of the gas model and the generating function of directed animals counted according to the area. This provides some new methods to compute the generating function of directed animals counted according to area, and leads in the particular case of the square lattice to new combinatorial results and questions. A model of gas related to directed animals counted according to area and perimeter on any directed graph is also exhibited.