Whitney Numbers for Poset Cones

@article{DorpalenBarry2021WhitneyNF,
  title={Whitney Numbers for Poset Cones},
  author={Galen Dorpalen-Barry and Jang Soo Kim and Victor Reiner},
  journal={Order},
  year={2021},
  volume={38},
  pages={283-322}
}
Hyperplane arrangements dissect ℝ n $\mathbb {R}^{n}$ into connected components called chambers, and a well-known theorem of Zaslavsky counts chambers as a sum of nonnegative integers called Whitney numbers of the first kind. His theorem generalizes to count chambers within any cone defined as the intersection of a collection of halfspaces from the arrangement, leading to a notion of Whitney numbers for each cone. This paper focuses on cones within the braid arrangement, consisting of the… 
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