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http://hdl.handle.net/10773/15081
Title: | The braid and the Shi arrangements and the Pak–Stanley labelling |
Author: | Duarte, Rui Guedes de Oliveira, António |
Keywords: | Parking functions Shi arrangement Braid arrangement |
Issue Date: | Nov-2015 |
Publisher: | Elsevier |
Abstract: | In this article we study a construction, due to Pak and Stanley, with which every region RR of the Shi arrangement is (bijectively) labelled with a parking function λ(R). In particular, we construct an algorithm that returns R out of λ(R). This is done by relating λ to another bijection, that labels every region S of the braid arrangement with r(S), the unique central parking function f such that λ−1(f)⊆S. We also prove that λ maps the bounded regions of the Shi arrangement bijectively onto the prime parking functions. Finally, we introduce a variant (that we call “s-parking”) of the parking algorithm that is in the very origin of the term “parking function”. S-parking may be efficiently used in the context of our new algorithm, but we show that in some (well defined) cases it may even replace it. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/15081 |
DOI: | 10.1016/j.ejc.2015.03.017 |
ISSN: | 1095-9971 |
Appears in Collections: | CIDMA - Artigos AGG - Artigos |
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