Bijections for the Shi and Ish arrangements
نویسندگان
چکیده
منابع مشابه
The Shi arrangement and the Ish arrangement
This paper is about two arrangements of hyperplanes. The first — the Shi arrangement — was introduced by Jian-Yi Shi to describe the Kazhdan-Lusztig cells in the affine Weyl group of type A. The second — the Ish arrangement — was recently defined by the first author who used the two arrangements together to give a new interpretation of the q, t-Catalan numbers of Garsia and Haiman. In the prese...
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We generalize a known bijection between the regions of the Shi and Ish hyperplane arrangements to a bijection between the regions of the nested-Ish and extendedShi arrangements. Although our bijection does not preserve the degrees of freedom statistic, we show that several of the steps do preserve this information, and we give formulas for the number of regions of each arrangement with a given ...
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LetW be a finite irreducible real reflection group, which is a Coxeter group. A primitive derivation D, introduced and studied by K. Saito (e.g., [4]), plays a crucial role in the theory of differential forms with logarithmic poles along the Coxeter arrangement. For example, we may describe the contact order filtration of the logarithmic derivation module using the primitive derivations ([10, 1...
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We present some contructions on the set of nbcs (No Broken Circuit sets) of some deformations of the braid arrangement. This leads us to some new bijective proofs for Shi, Linial and similar hyperplane arrangements. Mathematics Subject Classifications (2000): Primary 05C22; Secondary 05C15.
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this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2014
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2013.12.001