Results 1 to 10 of about 3,293 (95)
On the Topology of the Cambrian Semilattices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 For an arbitrary Coxeter group $W$, David Speyer and Nathan Reading defined Cambrian semilattices $C_{\gamma}$ as certain sub-semilattices of the weak order on $W$.
Myrto Kallipoliti, Henri Mühle
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Sortable Elements for Quivers with Cycles [PDF]
The Electronic Journal of Combinatorics, 2010 Each Coxeter element $c$ of a Coxeter group $W$ defines a subset of $W$ called the $c$-sortable elements. The choice of a Coxeter element of $W$ is equivalent to the choice of an acyclic orientation of the Coxeter diagram of $W$. In this paper, we define a more general notion of $\Omega$-sortable elements, where $\Omega$ is an arbitrary orientation ...
Reading, Nathan, Speyer, David E.
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Tilting theory of preprojective algebras and c-sortable elements [PDF]
Journal of Algebra, 2018 For a finite acyclic quiver $Q$ and the corresponding preprojective algebra $Π$, we study the factor algebra $Π_w$ associated with a element $w$ in the Coxeter group introduced by Buan-Iyama-Reiten-Scott. The algebra $Π_w$ has a natural $\mathbb{Z}$-grading, and we prove that $\underline{\mathsf{Sub}}^{\mathbb{Z}}Π_w$ has a tilting object $M$. Moreover,
Yuta Kimura
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Sortable elements and Cambrian lattices [PDF]
Algebra Universalis, 2007 We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements.
Nathan Reading
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Sustaining the collaborative chronic care model in outpatient mental health: a matrixed multiple case study [PDF]
Implementation ScienceBackground Sustaining evidence-based practices (EBPs) is crucial to ensuring care quality and addressing health disparities. Approaches to identifying factors related to sustainability are critically needed.
Bo Kim +8 more
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C-sortable words as green mutation sequences
Proceedings of the London Mathematical Society, 2015 Let $Q$ be an acyclic quiver and $\mathbf{s}$ be a sequence with elements in the vertex set $Q_0$. We describe an induced sequence of simple (backward) tilting in the bounded derived category $\mathcal{D}(Q)$, starting from the standard heart $\mathcal{H}
Yu Qiu
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Discrete Mathematics & Theoretical Computer Science, 2020 The main objects of noncrossing Catalan combinatorics associated to a finite Coxeter system are noncross- ing partitions, sortable elements, and cluster complexes. The first and the third of these have known Fuss–Catalan generalizations.
Christian Stump +2 more
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Geochemistry of Surface Sediments From the Emperor Seamount Chain, North Pacific
Frontiers in Earth Science, 2021 Investigating the composition and distribution of pelagic marine sediments is fundamental in the field of marine sedimentology. The spatial distributions of surface sediment are unclear due to limited investigation along the Emperor Seamount Chain of the
Jie Chen +18 more
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Sortable elements in infinite Coxeter groups [PDF]
Transactions of the American Mathematical Society, 2010 In a series of previous papers, we studied sortable elements in finite Coxeter groups, and the related Cambrian fans. We applied sortable elements and Cambrian fans to the study of cluster algebras of finite type and the noncrossing partitions associated to Artin groups of finite type.
Reading, Nathan, Speyer, David E.
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Partition and composition matrices: two matrix analogues of set partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 This paper introduces two matrix analogues for set partitions; partition and composition matrices. These two analogues are the natural result of lifting the mapping between ascent sequences and integer matrices given in Dukes & Parviainen (2010).
Anders Claesson +2 more
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