7 citations · 7 across the 3 of their papers we have counts for
5 papers
Expanding the quasisymmetric Macdonald polynomials in the fundamental basis
Sylvie Corteel, Olya Mandelshtam, Austin Roberts
The quasisymmetic Macdonald polynomials were recently introduced by the first and second authors with Haglund, Mason, and Williams in [3] to refine the symmetric Mac…
From symmetric fundamental expansions to Schur positivity
Austin Roberts
We consider families of quasisymmetric functions with the property that if a symmetric function is a positive sum of functions in one of these families, then f is necessarily a…
Coxeter-Knuth graphs and a signed Little map for type B reduced words
Sara Billey, Zachary Hamaker, Austin Roberts +1
We define an analog of David Little's algorithm for reduced words in type B, and investigate its main properties. In particular, we show that our algorithm preserves the recording…
On the Schur expansion of Hall-Littlewood and related polynomials via Yamanouchi words
Austin Roberts
This paper uses the theory of dual equivalence graphs to give explicit Schur expansions for several families of symmetric functions. We begin by giving a combinatorial definition o…
Dual Equivalence Graphs Revisited and the Explicit Schur Expansion of a Family of LLT Polynomials
Austin Roberts
In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph wh…