A PARTIAL ORDER ON THE ORTHOGONAL GROUP

By Tom D. Brady, Colum Watt. 2002

59 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Food Science, Management Information Systems

View Paper: https://www.semanticscholar.org/paper/a5f8f3a936e9e88ad541fcdbab23055ba461e727

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Food Science

In Management Information Systems

Citations in the corpus

Sortable elements in infinite Coxeter groups (2008, background): “crossing partition lattice in W (with respect to the Coxeter element c) is the interval [1,c]T in the partial order “≤T.” The elements of this interval are called c-noncrossing partitions. Results of [9] show that a noncrossing partition is uniquely determined by its ﬁxed space and that the ﬁxed spa”
Foundations of Garside Theory (2013, methodology): “4 in t he case whenG is a (general) finite Coxeter group, following the approach of Br ady and Watt in [30].”
Clusters, Coxeter-sortable elements and noncrossing partitions (2005, background): “In this section we present background on noncrossing partitions based on [3, 7].”
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (2006, methodology): “We have based this introduction on results of Carter [39], Brady and Watt [34, 35] and Bessis [17].”
Noncrossing partitions and the shard intersection order (2009, background): “oup of orthogonal transformations of the Euclidean vector space V. Let Fix : W → Int(A(W)) be the map taking w∈ Wto the subspace of V consisting of points ﬁxed by w. The following facts are proved in [8] and [9, Section 2]: The restriction of the map Fix to [1,c]T is injective; we call the subspaces”
Non-crossing partition lattices in finite real reflection groups (2007, unknown): “We note that the partial order on W is the restriction to W of a partial order on the orthogonal group O(n) which is introduced in [ 9 ] and investigated further in [10].”
K(π, 1) for Artin Groups of Finite Type (2002, methodology): “It is shown in [5] that |M(AC)| ≤ |M(A)|+ |M(C)|”
Cyclic Sieving of Noncrossing Partitions for Complex Reflection Groups (2007, methodology): “ard inclusion NC(W)∩W′ ⊆ NC(W′) in Lemma 3.3 is straightforward and proven in the next subsection, using the elementary linear algebraic interpretation of the partial order on W due to Brady and Watt [11]. The reverse inclusion appears harder, and is proven in the following subsection. It uses the g”
K(π 1)'s for Artin Groups of Finite Type (2000, methodology): “This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License K(π, 1)’S FOR ARTIN GROUPS OF FINITE TYPE THOMAS BRADY AND COLUM WATT”
Surveys in Combinatorics 2011: The cyclic sieving phenomenon: a survey (2010, background): “As defined by Brady and Watt in the real case [9] and Bessis in the complex [5, 6], the noncrossing elements in W are NC(W ) = {w ∈W : lR(w) + lR(w g) = lR(g)}.”
The dual braid monoid (2001, result): “The next proposition summarizes the main results from [ 6 ]; it is a refinement of Lemma 1.2.1.”