Jack characters and enumeration of maps

TL;DR

This paper presents explicit formulas for the leading part of Jack characters, linking them to bicolored oriented maps with arbitrary face structures, thus advancing the combinatorial understanding of Jack symmetric functions.

Contribution

It introduces explicit formulas for the top-degree part of Jack characters using bicolored oriented maps, a novel combinatorial approach.

Findings

Explicit formulas for top-degree Jack characters.

Connection between Jack characters and bicolored maps.

Enhanced combinatorial understanding of Jack symmetric functions.

Abstract

Jack characters provide dual information about Jack symmetric functions. We give explicit formulas for the top-degree part of these Jack characters in terms of bicolored oriented maps with an arbitrary face structure.