Kurt Luoto
A combinatorial characterization of tight fusion frames.
Thu, 12/15/2011 - 15:01 — SomNambulAuthors: Edward Richmond, Kurt Luoto, Marcin Bownik
Subjects: Functional Analysis
AbstractIn this paper we give a combinatorial characterization of tight fusion frame
(TFF) sequences using Littlewood-Richardson skew tableaux. The equal rank case
has been solved recently by Casazza, Fickus, Mixon, Wang, and Zhou. Our
characterization does not have this limitation. We also develop some methods
for generating TFF sequences. The basic technique is a majorization principle
for TFF sequences combined with spatial and Naimark dualities. We use these
methods and our characterization to give necessary and sufficient conditions
which are satisfied by the first three highest ranks.- Read more
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Skew quasisymmetric Schur functions and noncommutative Schur functions.
Thu, 07/08/2010 - 15:01 — SomNambulAuthors: Stephanie van Willigenburg, Christine Bessenrodt, Kurt Luoto
Subjects: Combinatorics
AbstractRecently a new basis for the Hopf algebra of quasisymmetric functions $QSym$,
called quasisymmetric Schur functions, has been introduced by Haglund, Luoto,
Mason, van Willigenburg. In this paper we extend the definition of
quasisymmetric Schur functions to introduce skew quasisymmetric Schur
functions. These functions include both classical skew Schur functions and
quasisymmetric Schur functions as examples, and give rise to a new poset
$\mathcal{L}_C$ that is analogous to Young's lattice. We also introduce a new
basis for the Hopf algebra of noncommutative symmetric functions $NSym$.
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