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Counting Shi regions with a fixed separating wall

Abstract : Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant regions which have the fixed hyperplane as a separating wall; that is, regions where the hyperplane supports a facet of the region and separates the region from the origin.
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Susanna Fishel, Eleni Tzanaki, Monica Vazirani. Counting Shi regions with a fixed separating wall. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.351-362. ⟨hal-01215106⟩

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