Counting Shi regions with a fixed separating wall

Details Counting Shi regions with a fixed separating wall Counting Shi regions with a fixed separating wall

2012-02-29

arxiv.org/abs/1202.6648v1

Mathematics

Combinatorics

To appear in Annals of Combinatorics

Scientific paper

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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