Multigraph Hyperplane Arrangements and Parking Functions

Hyperplane Arrangements, Parking Functions and Tree Inversions

Orientations, Semiorders, Arrangements, and Parking Functions

It is known that the Pak-Stanley labeling of the Shi hyperplane arrangement provides a bijection between the regions of the arrangement and parking functions. For any graph G, we define the G-semiorder arrangement and show that the Pak-Stanley labeling of its regions produces all G-parking functions. In his study of Kazhdan-Lusztig cells of the affine Weyl group of typeAn−1, [10], J.-Y. Shi int...

Functions of random walks on hyperplane arrangements

Article history: Received 14 December 2009 Accepted 5 February 2010 Available online 24 March 2010 MSC: primary 60J10 secondary 52C35

Random Walk and Hyperplane Arrangements

Let C be the set of chambers of a real hyperplane arrangement. We study a random walk on C introduced by Bidigare, Hanlon, and Rockmore. This includes various shuuing schemes used in computer science, biology, and card games. It also includes random walks on zonotopes and zonotopal tilings. We nd the stationary distributions of these Markov chains, give good bounds on the rate of convergence to...

Branched Polymers and Hyperplane Arrangements

We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie [BI], and Kenyon and Winkler [KW] to any hyperplane arrangement A. The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A is expressed through the value of the chara...