关于三角域上的游动数
On the Number of Walks in a Triangular Domain
摘要：
我们考虑行走的三角形域是一个子集的三角形格。然后，我们专门通过将格划分为两个有向子格具有不同的权重。我们的中心结果是一个明确的公式开始于一个不动点在这个域中的生成函数的散步和结束的域内的任何地方。有趣的是，这个公式专门用于从三角形的一个固定角开始的行走，这表明在有限高度的条带中，这些路径与双色Motzkin路径和双色三候选选票路径是等量的。
英文摘要：
We consider walks on a triangular domain that is a subset of the triangular lattice. We then specialise this by dividing the lattice into two directed sublattices with different weights. Our central result is an explicit formula for the generating function of walks starting at a fixed point in this domain and ending anywhere within the domain. Intriguingly, the specialisation of this formula to walks starting in a fixed corner of the triangle shows that these are equinumerous to two-coloured Motzkin paths, and two-coloured three-candidate Ballot paths, in a strip of finite height.
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。
