Results 1 to 10 of about 19,951 (83)
Hyperfactord of Shi Arrangement Sh(A2) and Sh(A3)
Mustansiriyah Journal of Science, 2022 In this paper, we introduce the region and the faces poset of shi arrangement that J. Y. Shi firstly introduced it. This is an affine arrangement, each of whose hyperplane is parallel to some"hyperplane of Coxeter arrangement"(Braid arrangement), the ...
Alaa A. A. Al-Mujmaey +1 more
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The Shi Arrangement and the Ish Arrangement [PDF]
Discrete Mathematics and Theoretical Computer Science, 2011 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.
Brendon Patrick Rhoades
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Bijections of Dominant Regions in the m-Shi Arrangements of Type A, B and C [PDF]
Discrete Mathematics and Theoretical Computer Science, 2015 In the present paper, the relation between the dominant regions in the $m$-Shi arrangement of types $B_n/C_n$, and those of the $m$-Shi arrangement of type $A_{n-1}$ is investigated. More precisely, it is shown explicitly how the sets $R^m(B_n)$ and $R^m(
Eleni Tzanaki
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Commentary on the Song Dynasty Incomplete Block-printed Edition of the Men Lei Zeng Guang Shi Zhu Du Gong Bu Shi in the National Library of China [PDF]
Journal of Library and Information Studies, 2022 The Men Lei Zeng Guang Shi Zhu Du Gong Bu Shi (門類增廣十注杜工部詩) collected by National Library of China, is one of the rare surviving editions of Song dynasty.
Qi-Xiu Zhang, Wei Sun
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Prioritization of the Eelements Affecting Urban Environmental Quality in Shiraz [PDF]
برنامه ریزی فضایی, 2022 Urban environmental quality as a part of the urban life quality has a special position in contemporary urban planning studies because the higher the quality of an urban environment is, the higher the potential for smart and sustainable development will ...
Mahshid MohammadEbrahimi +1 more
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Counting Shi regions with a fixed separating wall [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 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 ...
Susanna Fishel +2 more
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The freeness of Ish arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q; t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement ...
Takuro Abe +2 more
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Hyperplane Arrangements and Diagonal Harmonics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 In 2003, Haglund's bounce statistic gave the first combinatorial interpretation of the q,t-Catalan numbers and the Hilbert series of diagonal harmonics. In this paper we propose a new combinatorial interpretation in terms of the affine Weyl group of type
Drew Armstrong
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Bigraphical arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson.
Sam Hopkins, David Perkinson
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$q,t$-Fuß-Catalan numbers for complex reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 In type $A$, the $q,t$-Fuß-Catalan numbers $\mathrm{Cat}_n^{(m)}(q,t)$ can be defined as a bigraded Hilbert series of a module associated to the symmetric group $\mathcal{S}_n$.
Christian Stump
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