4 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 theo…
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 note on the map expansion of Jack polynomials
Houcine Ben Dali
In a recent work, Maciej Dołe\k{}ga and the author have given a formula of the expansion of the Jack polynomial in the power-sum basis as a non-orientability generating…
Integrality in the Matching-Jack conjecture and the Farahat-Higman algebra
Houcine Ben Dali
Using Jack polynomials, Goulden and Jackson have introduced a one parameter deformation of the generating series of bipartite maps, which generalizes the partition function o…