5 papers
Macdonald characters from a new formula for Macdonald polynomials
Houcine Ben Dali, Michele D'Adderio
We introduce a new operator on symmetric functions, which enables us to obtain a creation formula for Macdonald polynomials. This formula provides a connection between the the…
A probabilistic interpretation for interpolation Macdonald polynomials
Houcine Ben Dali, Lauren Williams
Previous work of Ayyer, Martin, and Williams gave a probabilistic interpretation of the Macdonald polynomials at in terms of a Markov chain called t…
Differential equations for the series of hypermaps with control on their full degree profile
Houcine Ben Dali
We consider the generating series of oriented and non-oriented hypermaps with controlled degrees of vertices, hyperedges and faces. It is well known that these series have natural…
A combinatorial formula for Interpolation Macdonald polynomials
Houcine Ben Dali, Lauren Williams
In 1996, Knop and Sahi introduced a remarkable family of inhomogeneous symmetric polynomials, defined via vanishing conditions, whose top homogeneous parts are exactly the Macdonal…
Path operators and -tau functions
Houcine Ben Dali, Valentin Bonzom, Maciej DoÅÄga
We construct a new class of operators that act on symmetric functions with two deformation parameters and . Our combinatorial construction associates each operator with a sp…