Strong and powerful P-tableaux are conjectured to give lower and upper bounds for e-coefficients of chromatic symmetric functions, with exact interpretations proven for several families.
Noncommutative Schur functions, switchboards, and Schur positivity
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Toward Lower Bounds for Chromatic Symmetric Functions in the Elementary Basis
Strong and powerful P-tableaux are conjectured to give lower and upper bounds for e-coefficients of chromatic symmetric functions, with exact interpretations proven for several families.