图的双射拓扑递归
A bijective topological recursion for maps
AI总结：
该研究双射证明任意拓扑图的递归切除公式，扩展至带自回避环模型的图和填充图，为拓扑递归项赋予组合意义，构造基于迭代 Tutte 算法，提供 Mirzakhani-McShane 恒等式的图类似物。
AI中文摘要：
我们双射地证明了任意拓扑图的递归切除公式，这得到了支配其计数的拓扑递归公式，该公式已在形式生成级数层面给出，且无需任何解析性假设。我们将该结果扩展到带有自回避环模型的图和填充图（即允许任意拓扑面的图变体）。我们的结果为（填充）图已知的（带 blob 的）拓扑递归的所有项赋予了精确的组合意义，包括此前缺失的递归核。该构造依赖于迭代 Tutte 算法直至拓扑发生变化的简单思路，等价地，可将其解释为由第一个边界根出发的路径驱动的裤分解，为图提供了双曲曲面的 Mirzakhani-McShane 恒等式的类似物。
英文摘要：
We prove bijectively a recursive excision formula for maps of arbitrary topology. This yields the topological recursion formulae governing their enumeration, already at the level of formal generating series and without any analyticity assumption. We extend the result to maps carrying self-avoiding loop models and to stuffed maps, i.e. a variant of maps allowing faces of arbitrary topology. Our results give a precise combinatorial meaning to all terms of the (blobbed) topological recursion known for (stuffed) maps, including the recursion kernel, which had so far been missing. The construction relies on the simple idea of iterating Tutte's algorithm until the topology changes. Equivalently, it can be interpreted as a pair-of-pants decomposition driven by a path issuing from the root of the first boundary, providing an analogue for maps of the Mirzakhani-McShane identity for hyperbolic surfaces.
