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Counting Shi Regions with a Fixed Separating Wall |
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| Authors: | Susanna Fishel Eleni Tzanaki Monica Vazirani |
| Institution: | 1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA 2. Department of Applied Mathematics, University of Crete, 71409, Heraklion, Crete, Greece 3. Department of Mathematics, UC Davis, UC Davis, CA, 95616, USA |
| 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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