Results 21 to 30 of about 904,790 (255)
Posets, parking functions and the regions of the Shi arrangement revisited
, 2011 15 pages, 7 ...
Karola Meszaros
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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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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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Decorous lower bounds for minimum linear arrangement [PDF]
, 2011 Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice.
Salazar, J J, Caprara, A, Letchford, A N
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Shi Threshold Arrangement [PDF]
The Electronic Journal of Combinatorics, 2012 Richard Stanley suggested the problem of finding the number of regions and the characteristic polynomial of a certain hyperplane arrangement defined by $x_i + x_j=0,1$, which is called the Shi threshold arrangement. We present the answer of the problem, using the finite field method.
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The freeness of Shi–Catalan arrangements
European Journal of Combinatorics, 2011 12 ...
Takuro Abe, Hiroaki Terao
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