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Franco Saliola

  1. Spectra of Symmetrized Shuffling Operators.

    Втр, 02/15/2011 - 16:01 — SomNambul
    Authors: Franco Saliola, Volkmar Welker, Victor Reiner
    Subjects: Combinatorics
    Abstract

    (Abridged abstract) For a finite real reflection group W and a W-orbit O of
    flats in its reflection arrangement---or equivalently a conjugacy class of its
    parabolic subgroups---we introduce a statistic on elements of W. We then study
    the operator of right-multiplication within the group algebra of W by the
    element whose coefficients are given by this statistic.

  2. Primitive orthogonal idempotents for R-trivial monoids.

    Втр, 09/28/2010 - 15:01 — SomNambul
    Authors: Franco Saliola, Chris Berg, Nantel Bergeron, Sandeep Bhargava
    Subjects: Representation Theory
    Abstract

    We show that the notions of $R$-trivial monoid and weakly ordered monoid are
    equivalent. We use this fact to construct a complete system of orthogonal
    idempotents for all $R$-trivial monoids.

  3. Oriented Interval Greedoids.

    Втр, 09/08/2009 - 12:16 — SomNambul
    Authors: Franco Saliola, Hugh Thomas
    Subjects: Combinatorics
    Abstract

    We propose a definition of an "oriented interval greedoid" that
    simultaneously generalizes the notion of an oriented matroid and the
    construction on antimatroids introduced by L. J. Billera, S. K. Hsiao, and J.
    S. Provan in "Enumeration in convex geometries and associated polytopal
    subdivisions of spheres" [Discrete Comput. Geom. 39 (2008), no. 1-3, 123--137].
    As for of oriented matroids, associated to each oriented interval greedoid is a
    spherical simplicial complex whose face enumeration depends only on the
    underlying interval greedoid.

  4. Oriented Interval Greedoids.

    Втр, 09/08/2009 - 12:16 — SomNambul
    Authors: Franco Saliola, Hugh Thomas
    Subjects: Combinatorics
    Abstract

    We propose a definition of an "oriented interval greedoid" that
    simultaneously generalizes the notion of an oriented matroid and the
    construction on antimatroids introduced by L. J. Billera, S. K. Hsiao, and J.
    S. Provan in "Enumeration in convex geometries and associated polytopal
    subdivisions of spheres" [Discrete Comput. Geom. 39 (2008), no. 1-3, 123--137].
    As for of oriented matroids, associated to each oriented interval greedoid is a
    spherical simplicial complex whose face enumeration depends only on the
    underlying interval greedoid.

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