Results 31 to 40 of about 19,462 (147)
$q,t$-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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, 2018 We introduce a new family of hyperplane arrangements in dimension n≥3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of a given subfamily have the same number of regions – the connected components of the ...
Duarte, Rui +1 more
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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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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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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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A bijection between dominant Shi regions and core partitions [PDF]
, 2009 It is well-known that Catalan numbers Cn=1n+1(2nn) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n+1)-cores.
Susanna Fishel +3 more
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