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On Whitney Numbers of the First and Second Kind, or is it the Other Way Around? -
The Whitney numbers of the first and second kind are a pair of poset invariants that are relevant in various areas of mathematics. One of the most interesting appearances of these numbers is as the coefficients of the chromatic polynomial of a graph. They also appear as counting regions in the complement of a real hyperplane arrangement. In this talk, I will introduce these concepts and will share a very curious phenomenon: sometimes the Whitney numbers of the first and second kind of a poset happen to be also the Whitney numbers of the second and first kind but of a different poset. To find examples of this phenomenon we rely on the poset technique of edge labelings. The results and open questions that will be presented are joint work with Josh Hallam, Yeison Quiceno, and José Samper.
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