A -multinomial expansion of LLT coefficients and plethysm multiplicities

Lascoux, Leclerc and Thibon (1997) [9] introduced a family of symmetric polynomials, called LLT polynomials. We prove a q -multinomial expansion of the coefficients of LLT polynomials in the case where μ = ( μ , ⋯ , μ ) ︸ n and define a q -analog of a sum of the plethysm multiplicities.