Results 21 to 30 of about 19,463 (248)
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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The Shi arrangement and the Ish arrangement [PDF]
Transactions of the American Mathematical Society, 2012 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 ...
Rhoades, Brendon +3 more
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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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Case Studies in Thermal Engineering, 2021 This research investigates the effects of using aligned/staggered arrangements of cooling units and top aisles containments on the performance of in-rows cooling architectures of data centers.
A.M. Abbas +3 more
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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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