Counting faces in the extended Shi arrangement
نویسندگان
چکیده
منابع مشابه
A Labelling of the Faces in the Shi Arrangement
Let Fn be the face poset of the n-dimensional Shi arrangement, and let Pn be the poset of parking functions of length n with the order defined by (a1, a2, . . . , an) ≤ (b1, b2, . . . , bn) if ai ≤ bi for all i. Pak and Stanley constructed a labelling of the regions in Fn using the elements of Pn. We show that under this labelling, all faces in Fn correspond naturally to closed intervals of Pn,...
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The number of regions of the type Cn Shi arrangement in Rn is (2n + 1)n. Strikingly, no bijective proof of this fact has been given thus far. The aim of this paper is to provide such a bijection and use it to prove more refined results. We construct a bijection between the regions of the type Cn Shi arrangement in Rn and sequences a1a2 . . . an, where ai ∈ {−n,−n+1, . . . ,−1, 0, 1, . . . , n−1...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2019
ISSN: 0196-8858
DOI: 10.1016/j.aam.2019.05.002