论文标题
伯纳迪公式用于编织的非交易性变形
The Bernardi formula for non-transitive deformations of the braid arrangement
论文作者
论文摘要
贝尔纳迪（Bernardi）给出了一个通用公式，用于将辫子布置变形的区域数量作为盒装树上的签名总和。我们证明，每组共享一个基础（扎根的平面）树的盒装树对此和-1贡献0，+1或-1，我们给出了一种用于计算此值的算法。对于ISH类型的布置，我们进一步构建了一个反向签名的相互作用，将Bernardi的签名总和减少为一组（扎根标记的平面）树的枚举。我们通过明确列举与嵌套ISH型布置区域相对应的树木，以恢复其已知的计数公式。
Bernardi has given a general formula for the number of regions of a deformation of the braid arrangement as a signed sum over boxed trees. We prove that each set of boxed trees which share an underlying (rooted labeled plane) tree contributes 0, +1, or -1 to this sum, and we give an algorithm for computing this value. For Ish-type arrangements, we further construct a sign-reversing involution which reduces Bernardi's signed sum to the enumeration of a set of (rooted labeled plane) trees. We conclude by explicitly enumerating the trees corresponding to the regions of Ish-type arrangements which are nested, recovering their known counting formula.
