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- W2344656775 abstract "We establish counting formulas and bijections for deformations of the braid arrangement. Precisely, we consider real hyperplane arrangements such that all the hyperplanes are of the form $x_i-x_j=s$ for some integer $s$. Classical examples include the braid, Catalan, Shi, semiorder and Linial arrangements, as well as graphical arrangements. We express the number of regions of any such arrangement as a signed count of decorated plane trees. The characteristic and coboundary polynomials of these arrangements also have simple expressions in terms of these trees. We then focus on certain well-behaved deformations of the braid arrangement that we call transitive. This includes the Catalan, Shi, semiorder and Linial arrangements, as well as many other arrangements appearing in the literature. For any transitive deformation of the braid arrangement we establish a simple bijection between regions of the arrangement and a set of plane trees defined by local conditions. This answers a question of Gessel." @default.
- W2344656775 created "2016-06-24" @default.
- W2344656775 creator A5065660197 @default.
- W2344656775 date "2018-01-01" @default.
- W2344656775 modified "2023-09-27" @default.
- W2344656775 title "Deformations of the braid arrangement and Trees" @default.
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