装饰树

Pierrette Cassou-Noguès, Daniel Daigle
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引用次数: 0

摘要

我们研究的是一类组合对象,我们称之为 "装饰树"。它们由顶点、箭头和边组成,其中每条边由两个整数装饰(每个端点附近各一个),每个箭头由一个整数装饰,而且这些装饰必须满足某些条件。装饰树类包括代数几何中使用的不同类型的树,如奇点链接的艾森布德图和诺伊曼图,以及代数平面曲线无穷远链接的诺伊曼图。通过纯粹的组合手段,我们恢复了一些以前被理解为 "拓扑 "的公式。通过这种方式,我们扩展了这些公式的一般性,并证明它们实际上是 "组合式的"。
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Decorated trees
We study a class of combinatorial objects that we call ``decorated trees''. These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and the decorations are required to satisfy certain conditions. The class of decorated trees includes different types of trees used in algebraic geometry, such as the Eisenbud and Neumann diagrams for links of singularities and the Neumann diagrams for links at infinity of algebraic plane curves. By purely combinatorial means, we recover some formulas that were previously understood to be ``topological''. In this way, we extend the generality of those formulas and show that they are in fact ``combinatorial''.
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