Counting Shi regions with a fixed separating wall
Combinatorics
2012-03-01 v1
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.
Cite
@article{arxiv.1202.6648,
title = {Counting Shi regions with a fixed separating wall},
author = {Susanna Fishel and Eleni Tzanaki and Monica Vazirani},
journal= {arXiv preprint arXiv:1202.6648},
year = {2012}
}
Comments
To appear in Annals of Combinatorics