Following ideas that go back to Cannon, we show the rationality of various generating functions of growth sequences counting embeddings of convex subgraphs in locally-finite, vertex-transitive graphs with the (relative) falsification by fellow traveler property (fftp). In particular, we recover results of Cannon, of Epstein, Iano–Fletcher and Zwick, and of Calegari and Fujiwara. One of our applications concerns Schreier coset graphs of hyperbolic groups relative to quasi-convex subgroups, we show that these graphs have rational growth, the falsification by fellow traveler property, and the existence of a lower bound for the growth rate independent of the finite generating set and the infinite index quasi-convex subgroup.

中文翻译：

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计算具有对称性的fftp图中的子图

遵循可以追溯到 Cannon 的想法，我们展示了增长序列的各种生成函数的合理性，这些生成函数计算了局部有限、顶点传递图中凸子图的嵌入，并带有同伴旅行财产 (fftp) 的（相对）证伪。特别是，我们恢复了 Cannon、Epstein、Iano-Fletcher 和 Zwick 以及 Calegari 和 Fujiwara 的结果。我们的应用之一是关于双曲群相对于准凸子群的 Schreier 陪集图，我们证明这些图具有理性增长、被同行者财产证伪以及存在独立于有限生成的增长率的下界集和无限索引拟凸子群。