Counting Shi regions with a fixed separating wall - Susanna Fishel; Eleni Tzanaki; Monica Vazirani (Discrete Mathematics & Theoretical Computer Science, 2011)
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.