LLT cumulants of unicellular Young diagrams, parking functions and Schur positivity

Abstract

We give a combinatorial formula for LLT cumulants of unicellular unilevelled shapes in terms of parking functions and Cayley trees. Our formula implies previously conjectured Schur positivity.

References in corpus (3)

• A modular relation for the chromatic symmetric functions of (3+1)-free posets
• A combinatorial expansion of vertical-strip LLT polynomials in the basis of elementary symmetric functions
• Macdonald cumulants, $G$-inversion polynomials and $G$-parking functions

Cited by in corpus (1)

• LLT cumulants and graph coloring