Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials
Copyright policy )Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials
We present several new and compact formulas for the modified and integral form of the Macdonald polynomials, building on the compact "multiline queue" formula for Macdonald polynomials due to Corteel, Mandelshtam and Williams. We also introduce a new quasisymmetric analogue of Macdonald polynomials. These quasisymmetric Macdonald polynomials refine the (symmetric) Macdonald polynomials and specialize at $q=t=0$ to the quasisymmetric Schur polynomials defined by Haglund, Luoto, Mason, and van Willigenburg. This is an extended abstract.
10 pages, 4 figures
- French National Centre for Scientific Research France
- Wake Forest University United States
- Harvard University United States
- University of Waterloo Canada
- University of California, Berkeley United States
Symmetric functions and generalizations, [MATH] Mathematics [math], quasisymmetric polynomials, asymmetric simple exclusion process, tableaux, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, symmetric functions, Macdonald polynomials, Combinatorics (math.CO)
Symmetric functions and generalizations, [MATH] Mathematics [math], quasisymmetric polynomials, asymmetric simple exclusion process, tableaux, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, symmetric functions, Macdonald polynomials, Combinatorics (math.CO)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!