Results 11 to 20 of about 20,001 (120)
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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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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Type C parking functions and a zeta map [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We introduce type $C$ parking functions, encoded as vertically labelled lattice paths and endowed with a statistic dinv'. We define a bijection from type $C$ parking functions to regions of the Shi arrangement of type $C$, encoded as diagonally labelled ...
Robin Sulzgruber, Marko Thiel
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The freeness of Shi–Catalan arrangements
European Journal of Combinatorics, 2011 12 ...
Takuro Abe, Hiroaki Terao
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Parking Functions, Shi Arrangements, and Mixed Graphs [PDF]
The American Mathematical Monthly, 2015 The \emph{Shi arrangement} is the set of all hyperplanes in $\mathbb R^n$ of the form $x_j - x_k = 0$ or $1$ for $1 \le j < k \le n$. Shi observed in 1986 that the number of regions (i.e., connected components of the complement) of this arrangement is $(n+1)^{n-1}$.
Matthias Beck +5 more
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Bijections for the Shi and Ish arrangements
European Journal of Combinatorics, 2014 The {\sf Shi hyperplane arrangement} Shi(n) was introduced by Shi to study the Kazhdan-Lusztig cellular structure of the affine symmetric group. The {\sf Ish hyperplane arrangement} Ish(n) was introduced by Armstrong in the study of diagonal harmonics. Armstrong and Rhoades discovered a deep combinatorial similarity between the Shi and Ish arrangements.
Emily Leven +2 more
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The Shi arrangements and the Bernoulli polynomials [PDF]
Bulletin of the London Mathematical Society, 2011 We fixed a ...
Suyama, Daisuke, Terao, Hiroaki
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The Shi arrangement of the type $D_{\ell}$
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2012 In this paper, we give a basis for the derivation module of the cone over the Shi arrangement of the type $D_\ell$ explicitly.
Gao, Ruimei, Pei, Donghe, Terao, Hiroaki
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Evaluating the Potential of Organic Agriculture to Improve Soil Health and Reduce Environmental Impact [PDF]
SHS Web of ConferencesBiological agriculture is ahead of acknowledgment for its prospective to augment soil well-being and diminish environmental bearings associated with conservative agriculture. The crucial matter discussed in this investigation is the shortage of soil well-
Alabdeli Haider +2 more
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Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements [PDF]
Journal of Algebraic Combinatorics, 2015 In this article we prove that the ideal-Shi arrangements are free central arrangements of hyperplanes satisfying the dual-partition formula. Then it immediately follows that there exists a saturated free filtration of the cone of any affine Weyl arrangement such that each filter is a free subarrangement satisfying the dual-partition formula.
Abe, Takuro, Terao, Hiroaki
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