Results 21 to 30 of about 19,462 (147)
Vertex-weighted digraphs and freeness of arrangements between Shi and Ish [PDF]
European Journal of Combinatorics, 2021 We introduce and study a digraph analogue of Stanley's $ψ$-graphical arrangements from the perspectives of combinatorics and freeness. Our arrangements form a common generalization of various classes of arrangements in literature including the Catalan arrangement, the Shi arrangement, the Ish arrangement, and especially the arrangements interpolating ...
Takuro Abe, Tan Nhat Tran, Shuhei Tsujie
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Posets, parking functions and the regions of the Shi arrangement revisited [PDF]
, 2011 15 pages, 7 ...
Karola Meszaros
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Enumerating regions of Shi arrangements per Weyl cone [PDF]
European Journal of Combinatorics, 2023 Given a Shi arrangement $\mathcal{A}_Φ$, it is well-known that the total number of regions is counted by the parking number of type $Φ$ and the total number of regions in the dominant cone is given by the Catalan number of type $Φ$. In the case of the latter, Shi gave a bijection between antichains in the root poset of $Φ$ and the regions in the ...
Aram Dermenjian, 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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Bijections on r-Shi and r-Catalan arrangements [PDF]
Advances in Applied Mathematics, 2021 19 pages, 2 ...
Houshan Fu, Suijie Wang, Weijin Zhu
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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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Bijections for Faces of the Shi and Catalan Arrangements [PDF]
The Electronic Journal of Combinatorics, 2021 In 1986, Shi derived the famous formula $(n+1)^{n-1}$ for the number of regions of the Shi arrangement, a hyperplane arrangement in ${R}^n$. There are at least two different bijective explanations of this formula, one by Pak and Stanley, another by Athanasiadis and Linusson. In 1996, Athanasiadis used the finite field method to derive a formula for the
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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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