59 citations · 195 across the 22 of their papers we have counts for
16 papers · 1 filter
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…
-Hurwitz numbers from refined topological recursion
Nitin Kumar Chidambaram, Maciej Dołęga, Kento Osuga
We prove that single -weighted -Hurwitz numbers with internal faces are computed by refined topological recursion on a rational spectral curve, for certain rationa…
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…
LLT cumulants and graph coloring
Maciej Dołęga, Maciej Kowalski
The purpose of this note is to introduce a new family of quasi-symmetric functions called LLT cumulants and discuss its properties. We define LLT cumulants using the algebraic fram…
Blossoming bijection for bipartite pointed maps and parametric rationality of general maps of any surface
Maciej Dołęga, Mathias Lepoutre
We construct an explicit bijection between bipartite pointed maps of an arbitrary surface , and specific unicellular blossoming maps of the same surface. Our bijection…
A positive combinatorial formula for symplectic Kostka-Foulkes polynomials I: Rows
Maciej Dołęga, Thomas Gerber, Jacinta Torres
We prove a conjecture of Lecouvey, which proposes a closed, positive combinatorial formula for symplectic Kostka-Foulkes polynomials, in the case of rows of arbitrary weight. To sh…
Macdonald cumulants, -inversion polynomials and -parking functions
Maciej Dołęga
We prove a combinatorial formula for Macdonald cumulants which generalizes the celebrated formula of Haglund for Macdonald polynomials. We provide several applications of our formu…
Top degree part in -conjecture for unicellular bipartite maps
Maciej Dołęga
Goulden and Jackson (1996) introduced, using Jack symmetric functions, some multivariate generating series with an additional parameter that may be interpr…
Cumulants of Jack symmetric functions and -conjecture
Maciej Dołęga, Valentin Féray
Goulden and Jackson (1996) introduced, using Jack symmetric functions, some multivariate generating series that might be interpreted as a continuous deformatio…
A bijection for rooted maps on general surfaces
Guillaume Chapuy, Maciej Dołęga
We extend the Marcus-Schaeffer bijection between orientable rooted bipartite quadrangulations (equivalently: rooted maps) and orientable labeled one-face maps to the case of all su…
Jack polynomials and orientability generating series of maps
Maciej Dołęga, Valentin Féray, Piotr Śniady
We study Jack characters, which are the coefficients of the power-sum expansion of Jack symmetric functions with a suitable normalization. These quantities have been introduced by…
On Kerov polynomials for Jack characters
Maciej Dołęga, Valentin Féray
We consider a deformation of Kerov character polynomials, linked to Jack symmetric functions. It has been introduced recently by M. Lassalle, who formulated several conjectures on…
Polynomial functions on Young diagrams arising from bipartite graphs
Maciej Dołega, Piotr Śniady
We study the class of functions on the set of (generalized) Young diagrams arising as the number of embeddings of bipartite graphs. We give a criterion for checking when such a fun…
Characters of symmetric groups in terms of free cumulants and Frobenius coordinates
Maciej Dołega, Valentin Féray, Piotr Śniady
Free cumulants are nice and useful functionals of the shape of a Young diagram, in particular they give the asymptotics of normalized characters of symmetric groups S(n) in the lim…
Asymptotics of characters of symmetric groups: structure of Kerov character polynomials
Maciej Dołega, Piotr Śniady
We study asymptotics of characters of the symmetric groups on a fixed conjugacy class. It was proved by Kerov that such a character can be expressed as a polynomial in free cumulan…
Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations
Maciej Dołega, Valentin Féray, Piotr Sniady
We find an explicit combinatorial interpretation of the coefficients of Kerov character polynomials which express the value of normalized irreducible characters of the symmetric gr…