Compression Formula for Nonattacking Fillings of Non-symmetric Macdonald Polynomials

Source abstract

Macdonald polynomials are an important family of orthogonal polynomials that have applications to statistical physics. Corteel, Mandelshtam, and Williams proved a combinatorial model involving multiline queues for partitions; however, their work does not apply to weak compositions in general. We conjecture a first step towards this direction via a variant of the nonattacking filling model for nonsymmetric Macdonald Polynomials $E_μ$. This new model compresses the classical nonattacking filling model of Haglund, Haiman, and Loehr and mirrors the concept of trivial pairs in the multiline queue model. We prove it for a large family of weak compositions and explain the difficulty of extending this proof to the general case.