A note on the map expansion of Jack polynomials
The electronic journal of combinatorics, Tome 32 (2025) no. 3
In a recent work, Maciej Dołęga and the author have given a formula of the expansion of the Jack polynomial $J^{(\alpha)}_\lambda$ in the power-sum basis as a non-orientability generating series of bipartite maps whose edges are decorated with the boxes of the partition $\lambda$. We conjecture here a variant of this expansion in which we restrict the sum on maps whose edges are injectively decorated by the boxes of $\lambda$. We prove this conjecture for Jack polynomials indexed by 2-column partitions. The proof uses a mix of combinatorial methods and differential operator computations.
DOI :
10.37236/12535
Classification :
05E05, 05A15
Mots-clés : symmetric functions and generalizations, generating functions
Mots-clés : symmetric functions and generalizations, generating functions
Affiliations des auteurs :
Houcine Ben Dali 1
@article{10_37236_12535,
author = {Houcine Ben Dali},
title = {A note on the map expansion of {Jack} polynomials},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {3},
doi = {10.37236/12535},
zbl = {8097668},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12535/}
}
Houcine Ben Dali. A note on the map expansion of Jack polynomials. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/12535
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