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Showing 1 to 9 of 9 for “"Bruhat order"”.
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Double Affine Bruhat Order
… of a given element of W with respect to the Bruhat order, specifically when W is associated to a finite root system that is irreducible and simply laced. We show two approaches: one extending the work of Lam and Shimozono, and its strengthening by Milicevic, where cocovers are characterized …
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Permutation Patterns, Reduced Decompositions with Few Repetitions and the Bruhat Order
… used to classify and enumerate downsets in the Bruhat order for the symmetric group and the rook monoid which is a generalization of the symmetric group. Finally, motivated by coding theory, the concepts of displacement, additive stretch and multiplicative stretch of permutations are introduced. …
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A Combinatorially Explicit Relative Möbius Function on Affine Grassmannians and a Proposal for an Affine Infinite Symmetric Group
… the subposet of affine Grassmannians under the Bruhat order is non-zero by utilizing the quantum Bruhat graph of the classical Weyl group associated to W . Then we examine embedding stable and consistent statistics on the affine Weyl group of type A which permit the definition of an affine …
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Double affine galleries
… an infinite sequence of chambers, indexed by an ordered set, which is maximal with respect to a finiteness condition on the multiset of wall-crossings. We study the possible order types of galleries. We also use galleries to define a double affine Bruhat order which generalizes the one introduced …
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The combinatorics of reduced decompositions
… graphs and posets are explicitly determined. The Bruhat order for the symmetric group is examined, and the permutations with boolean principal order ideals are completely characterized. These form an order ideal which is a simplicial poset, and its rank generating function is computed. Moreover, …
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Exponential Random Graphs and a Generalization of Parking Functions
… parking functions have to various partial orders on the symmetric group on n letters including the (left) weak order, (strong) Bruhat order, and the bubble-sorting order.</p>
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On complex reflection groups G(m, 1, r) and their Hecke algebras
… condition for elements in a G(m, 1, r). A Bruhat order on the groups is also defined and investigated. We generalize the Geck-Pfeiffer reducibility theorem for finite Coxeter groups to the groups G(m, 1, r). Based on this, we prove that a character value of any element in an Ariki-Koike …
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Combinatorics of colored factorizations, flow polytopes and of matrices over finite fields
… diagram and Poincaré polynomials of the strong Bruhat order.
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On the geometry and parametrization of almost invariant subspaces and observer theory
… of fixed size, i.e. tracking observers of fixed order together with the functions they are tracking, is a smooth manifold. Furthermore, I construct a vector bundle structure for the set of conditioned invariant subspaces of fixed dimension together with their friends, i.e. the output injections …