Recently 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 weâ€¦ (More)

We refine the classical Littlewood-Richardson rule in several different settings. We begin with a combinatorial rule for the product of a Demazure atom and a Schur function. Building on this, we alsoâ€¦ (More)

We introduce a new basis for quasisymmetric functions, which arise from a specialization of nonsymmetric Macdonald polynomials to standard bases, also known as Demazure atoms. Our new basis is calledâ€¦ (More)

A new Z-basis for the space of quasisymmetric functions (QSym, for short) is presented. It is shown to have nonnegative structure constants, and several interesting properties relative to the spaceâ€¦ (More)

In 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 et al.â€¦ (More)

Problem 1.2 (Hilbertâ€™s nullstellensatz problem over a ring R). For a given ring R and positive integers n,m, let XR = R[x1, . . . , xn] and SR = {(f1, . . . , fm) âˆˆ X R | âˆƒ Î¶ âˆˆ R such that fi(Î¶) = 0â€¦ (More)

A new Z-basis for the space of quasisymmetric functions (QSym, for short) is presented. It is shown to have nonnegative structure constants, and several interesting properties relative to theâ€¦ (More)