5 papers
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 th…
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 Dołęga
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…
Positive formula for Jack polynomials, Jack characters and proof of Lassalle's conjecture
Houcine Ben Dali, Maciej Dołęga
We give an explicit formula for the power-sum expansion of Jack polynomials. We deduce it from a more general formula, which we provide here, that interprets Jack characters in ter…
Generating series of non-oriented constellations and marginal sums in the Matching-Jack conjecture
Houcine Ben Dali
Using the description of hypermaps with matchings, Goulden and Jackson have given an expression of the generating series of rooted bipartite maps in terms of the zonal polynomials.…