Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups

By Drew Armstrong. 2006

335 citations recorded by the source corpus.

Introduction Coxeter groups and noncrossing partitions $k$-divisible noncrossing partitions The classical types Fuss-Catalan combinatorics Bibliography.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b8d1a446def3fd4fe9871f5f8d7046dd646a4b90

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

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Citations in the corpus

Proof of the $$K(\pi , 1)$$ conjecture for affine Artin groups (2019, background): “The intervals [1, w] that arise from finite Coxeter groups W are well-studied, and are called (generalized) noncrossing partition lattices (see [Arm09]).”
A uniform bijection between nonnesting and noncrossing partitions (2011, background): “For a full exposition of this object and its history, see [1].”
A categorification of non-crossing partitions (2013, methodology): “We recall that non-crossing partitions were introduced by Kreweras [38] and later generalised in the context of Coxeter groups by Brady and Watt [7, 8], and independently by Bessis [4]; see also Armstrong’s memoir [1].”
Surveys in Combinatorics 2011: The cyclic sieving phenomenon: a survey (2010, background): “q = [4]q! [2]q![2]q! = [4]q[3]q [2]q = 1 + q + 2q(2) + q(3) + q(4).”
Cyclic Sieving of Noncrossing Partitions for Complex Reflection Groups (2007, neutral): “From this description, one immediately concludes that if a path γ′ : [0, 1] → V ′/W ′ −H′ is a tunnel (with respect to W ′), then, as a path in V/W −H (which contains V ′/W ′−H′), γ′ is also a tunnel (with respect to W ).”
Liberation of orthogonal Lie groups (2008, background): “y relaxing the easiness condition. This looks like a quite diﬃcult task, and we don’t know if this is really possible. Some evidence in this sense comes from the combinatorial results of Armstrong in [1]. (3) By using random matrices instead of quantum groups. The problem here is to understand the r”
Finite complex reflection arrangements are $K(\pi,1)$ (2006, neutral): “ligne’s element ∆. Choose v∈ Vreg such that the W-orbit vlies in L0. Brou´e-Malle-Rouquier consider the element (denoted by π, [21, Notation 2.3]) in the pure braid group P(W) represented by the loop [0,1] −→ Vreg t −→ vexp(2 √ −1πt). We prefer a diﬀerent notation: Deﬁnition 6.12. We call full-twist”
Parking Spaces (2012, positive): “To state these, first recall the q-number [n]q := 1+q+ · · ·+qn−1 the q-factorial [n]!q := [1]q[2]q · · · [n]q, and the q-binomial [ n k ]”