Between Shi and Ish
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...
متن کاملExtensions of the Shi/ish Duality
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 ...
متن کاملA bijection between dominant Shi regions and core partitions
It is well-known that Catalan numbers Cn = 1 n+1 ( 2n n ) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n + 1)-cores. These concepts have natural extensions, which we call here the m-Catalan numbers and m-Shi arrangement. In this paper, we construct a bijection between dominant regions of the m-Shi a...
متن کاملA bijection between (bounded) dominant Shi regions and core partitions
It is well-known that Catalan numbers Cn = 1 n+1 ( 2n n ) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n + 1)-cores. These concepts have natural extensions, which we call here the m-Catalan numbers and m-Shi arrangement. In this paper, we construct a bijection between dominant regions of the m-Shi a...
متن کاملStephanie Green ish
The forces experienced while surgically cutting anatomical tissues from a sheep and two rats were investigated for three scissor types. Data were collected in situ using instrumented Mayo, Metzenbaum, and Iris scissors immediately after death to minimize postmortem effects. The force-position relationship, the frequency components present in the signal, the signicance of the cutting rate, and ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2018
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.09.006