Macdonald polynomials for super-partitions

We discuss generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables: usual pk variables are accompanied by anti-commuting Grassmann variables θk. Starting from recently defined super-Schur polynomials and exploiting orthogonality relations with triangular decompositions we are able to fully determine super-Macdonald polynomials. These polynomials have similar properties to canonical Macdonald polynomials – they respect two different orderings in the set of (super)-Young diagrams simultaneously.