Resumen de On combinatorial formulas for Macdonald polynomials

Cristian Lenart

• A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of so-called alcove walks; these originate in the work of Gaussent�Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. In this paper, we relate the above developments, by explaining how the Ram�Yip formula compresses to a new formula, which is similar to the Haglund�Haiman�Loehr one but contains considerably fewer terms