Séminaire Lotharingien de Combinatoire, 89B.34 (2023), 12 pp.

Houcine Ben Dali and and Maciej Dołęga

Jack Characters as Generating Series of Bipartite Maps and Proof of Lassalle's Conjecture

Abstract. We give an explicit formula for the power-sum expansion of Jack polynomials. We deduce it from a more general formula that we provide here, that interprets Jack characters in terms of bipartite maps. Finally, we prove Lassalle's conjecture from 2008 on integrality and positivity of Jack characters in Stanley's coordinates.

Received: November 15, 2022. Accepted: February 20, 2023. Final version: April 1, 2023.

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