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Description: |
In 2005 Athanasiadis generalized the Narayana numbers by introducing the concept of separating wall for a region in the extended Shi arrangement. Using this concept, Susanna Fishel, Eleni Tzanaki and Monica Vazirani were able to calculate the number of dominant regions which have a fixed hyperplane as a separating wall, that is, regions where the fixed hyperplane supports a facet of the region and separates the region from the origin. In this talk we survey some combinatorial results about the extended Shi arrangement and present a bijective proof for the result described above. This is joint work with Eleni Tzanaki and Alessandro Conflitti.
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