Results 31 to 40 of about 20,001 (120)
Repetitions of Pak-Stanley labels in G-Shi arrangements
Discrete Mathematics33 pages, 8 figures, 13 ...
Cara Bennett +4 more
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A basis construction of the extended Catalan and Shi arrangements of the type A2
Journal of Algebra, 2018 In [9], Terao proved the freeness of multi-Coxeter arrangements with constant multiplicities by giving an explicit construction of bases. Combining it with algebro-geometric method, Yoshinaga proved the freeness of the extended Catalan and Shi arrangements in [11].
Takuro Abe, Daisuke Suyama
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International Journal of Nanomedicine, 2016 Ze-yuan Lei, Ting Liu, Wei-juan Li, Xiao-hua Shi, Dong-li Fan Department of Plastic and Cosmetic Surgery, XinQiao Hospital, The Third Military Medical University, ChongQing, People’s Republic of China Purpose: Silicone rubber implants have been ...
Lei ZY, Liu T, Li WJ, Shi XH, Fan DL
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Enumerating regions of Shi arrangements per Weyl cone
European Journal of CombinatoricsGiven 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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Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species
, 2019 19 ...
Nakashima, Norihiro, Tsujie, Shuhei
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On the two variable distance enumerator of the Shi hyperplane arrangement
European Journal of Combinatorics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Shi arrangements and low elements in Coxeter groups
Proceedings of the London Mathematical SocietyAbstractGiven an arbitrary Coxeter system and a non‐negative integer , the ‐Shi arrangement of is a subarrangement of the Coxeter hyperplane arrangement of . The classical Shi arrangement () was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for .
Dyer, Matthew +3 more
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Vertex-weighted digraphs and freeness of arrangements between Shi and Ish
European Journal of CombinatoricsWe 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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Asymmetric Catalan and Shi Hyperplane Arrangements
In this paper, we study the regions of asymmetric extensions of the Catalan and Shi arrangements. We first determine the characteristic polynomials using the finite field method, thereby obtaining explicit formulas for the number of regions. We then introduce two new classes of combinatorial objects: $\mathbf{c}$-labelled Dyck paths and $\mathbf{c ...
Biswas, Sucharita +2 more
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Drug Design, Development and TherapyQian Li,1,* Jing-Wen Zheng,1,* Zi-Yao Wang,1 Shi-Ping Liao,2 Ling Zhu,1 Xia Wang,3,* Li-Hong Wan1,4,* 1Department of Pharmacology, West China School of Basic Medical Sciences & Forensic Medicine, Sichuan University, Chengdu, Sichuan ...
Li Q +6 more
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